Advancing ASD diagnostic classification using time-frequency spectrograms of fMRI BOLD signals and machine learning

Advancing ASD diagnostic classification using time-frequency spectrograms of fMRI BOLD signals and machine learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Advancing ASD diagnostic classification using time-frequency spectrograms of fMRI BOLD signals and machine learning Tikaram Tikaram, Utkarsh Raj, Ravi Ratnaik, Jac Fredo Agastinose Ronickom This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5170177/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this study, our goal was to develop a diagnostic framework for autism spectrum disorder (ASD) by analyzing time-frequency spectrograms generated from BOLD signals in functional magnetic resonance imaging (fMRI) data. We used fMRI data from the Autism Brain Imaging Data Exchange (ABIDE) database and performed brain parcellation with Gordon’s, Harvard-Oxford, and Diedrichsen atlases. Time-frequency spectrograms were generated from the average time series of each region of interest (ROI) using methods like short-time Fourier transform, continuous wavelet transform, Mel frequency cepstrum (MFC), and smoothed pseudo Wigner-Ville distribution. From these spectrograms, we extracted various features, including the grey-level co-occurrence matrix, grey-level run-length matrix, fractal dimension texture analysis, Zernike moments, Hu moments, and first-order statistics. To evaluate the diagnostic model, we applied machine learning classifiers, including logistic regression, support vector machine (SVM), extreme gradient boosting, and random forest, alongside recursive feature elimination with 5-fold cross-validation (RFECV) and hyperparameter tuning. The SVM classifier using MFC spectrograms and RFECV yielded the highest performance, achieving an overall accuracy of 95.71%, sensitivity of 100%, specificity of 91.42%, F1-score of 95.76%, and area under the curve (AUC) of 95.71% with the top 36 features for the fronto-parietal task control network. In contrast, utilizing all 85 features for the somatosensory motor hand network resulted in an accuracy of 80.38%, sensitivity of 77.77%, specificity of 82.85%, F1-score of 80.27%, and AUC of 80.31%. These findings underscore the model's potential in the precise classification of ASD, offering valuable implications for early diagnosis and intervention. Autism spectrum disorder fMRI time-frequency spectrograms analysis feature extraction machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Autism spectrum disorder (ASD) is a persistent neurodevelopmental condition beginning in childhood, characterized by key impairments in social interaction, communication, and repetitive behaviours. These challenges are often linked to deficits in executive functions such as working memory, inhibition, cognitive flexibility, and planning. Affecting about 1 in 100 children worldwide, ASD requires customized therapeutic approaches due to its diverse manifestations and the lack of a definitive cure [ 1 ]. Early detection and intervention are crucial for alleviating symptoms and improving the quality of life for individuals with ASD. Diagnosis typically involves observation and input from parents, educators, and medical professionals, including pediatricians, child psychologists, neurologists, and therapists. Diagnosing ASD in adults is more challenging compared to older children and adolescents, due to symptom overlap with other mental health conditions. Although behavioural signs can appear as early as 6 months of age, the diagnostic process is complex, often leading to delays of several months to years because of the wide range of behaviours and subjective symptoms associated with ASD. Thus, there is a significant need for research into autism-specific brain imaging biomarkers to aid in early ASD detection [ 2 ]. Magnetic resonance imaging (MRI) is an essential tool for examining structural brain changes in children with ASD. Functional MRI (fMRI), specifically, has been extensively used to study overall brain function. These sophisticated imaging techniques can detect subtle alterations in brain metabolism and connectivity within neural networks over time, whether during cognitive tasks or resting-state brain activity. Blood-oxygen-level-dependent (BOLD) fMRI, which monitors changes in deoxyhemoglobin concentration, enables the visualization of neural metabolic changes linked to both cognitive tasks and spontaneous brain activity. In this study, we used resting-state fMRI data to find specific brain imaging biomarkers associated with ASD. Identifying distinct neural networks associated with ASD is crucial for uncovering biomarkers that can facilitate early and precise diagnosis. Numerous studies have attempted to pinpoint the brain networks affected in individuals with ASD. For instance, [ 4 ] highlighted the involvement of the cingulate gyri, superior temporal gyrus, and primary auditory cortex in ASD. Meanwhile, [ 5 ] observed variations in the angular gyrus, middle temporal gyrus, supramarginal gyrus, and paracingulate gyrus. Additionally, [ 6 ] determined that the retrosplenial temporal network provided the most reliable performance in ASD diagnostic classification. However, the specific brain regions or networks implicated in ASD have varied across studies. In our research, we have analysed a broad spectrum of brain regions across different networks to further explore the neurobiological mechanisms underlying ASD. Functional connectivity (FC) is the traditional approach for analysing fMRI signals, focusing on the temporal correlation of BOLD signals between distinct brain regions. Nonetheless, the BOLD signal is influenced by a range of physiological processes, including neuronal activity, metabolic functions, cardiac cycles, and levels of alertness, in addition to factors associated with imaging equipment and individual differences among participants. These influences introduce noise, which can compromise the accuracy of FC analysis results [ 3 ] [ 7 ]. Conversely, time-frequency methods break down signals in both the time and frequency domains, offering a more detailed perspective on signal behaviour in these domains simultaneously. Various time-frequency techniques, such as short-time Fourier transform (STFT), continuous wavelet transforms (CWT), discrete wavelet transform (DWT), Mel frequency cepstrum (MFC), Wigner-Ville distribution (WVD), smoothed pseudo Wigner-Ville distribution (SPWVD), Gabor-Wigner transform, Hilbert–Huang transform, and bilinear time-frequency distribution, have been employed for different applications [ 8 ]. The STFT operates similar to the Fourier transform but incorporates a window function and short wavelets localized in both time and frequency, using overlapping fixed-sized windows to calculate multiple traditional Fourier transforms [ 9 ]. The CWT addresses the limitations of the STFT by forgoing a window function and instead employing a family of base functions that adjust with frequency, thereby providing high resolution across the full frequency spectrum [ 10 ]. MFC spectrograms are created by converting the signal's linear frequency scale into a logarithmic Mel scale using STFT, followed by filtering through a filter bank to assess signal energy distribution across the Mel scale frequency range. The WVD offers a more concentrated energy representation of the signal compared to the STFT [ 11 ]. However, WVD is prone to cross-term interference, complicating the interpretation of its time-frequency representation [ 12 ]. To reduce this interference, the SPWVD is often used. This method is effective in analysing signal energy across time and frequency domains, offering insights into higher harmonics and precise localization in the time domain [ 8 ]. In this study, we compare the effectiveness of the STFT, CWT, MFC, and SPWVD methods in analysing fMRI BOLD signals for the diagnostic classification of ASD subjects. Extracting texture and moment-based features from spectrograms is vital for identifying specific patterns in fMRI BOLD signals associated with ASD. Commonly used techniques for quantifying texture information within images include the gray-level co-occurrence matrix (GLCM) and gray-level run-length matrix (GLRLM). GLCM examines the spatial relationships between pairs of pixels, while GLRLM assesses the length and orientation of sequences of contiguous pixels that share the same gray level. In addition, feature extraction from 2D signal representations involves methods such as fractal dimension texture analysis (FDTA), Zernike's moments (ZM), Hu's moments (HM), and first-order statistics (FOS). FDTA is especially effective for texture analysis as it evaluates the complexity and irregularity of patterns. ZM and HM are used to capture global and local shape characteristics within images, respectively. FOS involves metrics such as mean, variance, skewness, and kurtosis, which are often applied in extracting features from biological signals in biomedical research. In this study, we explored the use of features derived from spectrograms, including GLCM, GLRLM, HM, ZM, FDTA, and FOS, to aid in diagnosing ASD. Artificial intelligence, specifically through machine learning and deep learning techniques, is highly effective at handling complex, high-dimensional data and identifying underlying patterns in features to automate ASD diagnosis. A variety of machine learning approaches ranging from linear to non-linear models, as well as tree-based and ensemble methods have been widely applied in ASD diagnosis. Previous studies have employed machine learning classifiers including k-nearest neighbours (KNN) [ 18 ] [ 19 ], support vector machines (SVM) [ 18 ] [ 19 ] [ 5 ], decision trees, and categorical boosting [ 6 ], along with deep learning techniques [ 4 ] for classifying ASD. However, implementing deep learning algorithms often requires a large dataset and computationally powerful hardware. In this study, we utilized logistic regression (LR), extreme gradient boosting (XGBoost), SVM, and random forest (RF) for the diagnostic classification of ASD. The main contributions of this manuscript are Examined a large number of brain regions and networks to identify the neurobiological correlates of ASD. Analysed the effect of four different time-frequency methods STFT, CWT, MFC, and SPWVD in extracting patterns from fMRI BOLD signals Evaluated the impact of various texture features GLCM, GLRLM, FDTA, HM, ZM, and FOS in identifying patterns from the time-frequency spectrograms Implemented machine learning algorithms, such as LR, XGBoost, SVM and RF to automate the process of ASD diagnosis 2. Materials and Methods 2.1. Process pipeline The pipeline used in this study is demonstrated in Fig. 1 . The evaluation pipeline included (1) Preprocessing the fMRI data, (2) Parcellation of brain regions and extraction of BOLD signal, (3) Generate spectrograms using time-frequency methods, (4) Feature extraction, and (5) Feature selection was performed incorporating recursive feature elimination combined with cross-validation (RFECV) and classification using machine learning algorithms. 2.2 Dataset In this research, we acquired fMRI data from the open-access Autism Brain Imaging Data Exchange (ABIDE-I & ABIDE-II) datasets. It contains numerous resting-state fMRI, sMRI, and DTI of ASD as well as typically developing (TD) gathered from multiple global sites, with authorization of local institutional review boards [ 20 ]. This analysis focused on resting-state fMRI data from subjects with their eyes open, as the BOLD signals are influenced by the state of the eyes [ 21 ]. Further, images with at least 80% of original volumes retained after filtering, and root mean square deviation (motion) less than 0.2 were included in the analysis to avoid head movement effects on BOLD fluctuations [ 22 ]. We recorded participant diagnostic state, gender and age based on the demographic information mentioned in the dataset description. The age range of our participants were 7–15 years and 8–14 years old for ASD and TD respectively. 30 males, and 6 females subjects with ASD and 22 males and 13 females with TD individuals were included in our study from Oregon Health and Science University (OHSU) site. Demographic information of subjects considered in this study is summarized in Table 1 . Table 1 Demographic information Parameters ASD TD Number of subjects 36 35 Age in years (range) 13.57 ± 2.65 (7–15) 13.57 ± 2.65 (8–14) Gender ratio (M/F) 30/6 22/13 Handedness (R/L/M) 35/0/1 35/0/0 FIQ/VIQ/PIQ 106.19 ± 16.91 118.45 ± 12.17 M-Males, F-Females, R-Right, L-Left, M- Mixed handed, FIQ: Full Scale Intelligence Quotient, VIQ: Verbal Intelligent Quotient, PIQ: Performance Intelligence Quotient. 2.3 Preprocessing Resting-state fMRI data were preprocessed using the functional neuroimaging tools AFNI [ 23 ] and FSL 5.0 [ 24 ]. The preprocessing techniques in this study comprised seven key steps to improve the quality of the data. These steps are as follows: Trimming and Alignment: To start, initially fMRI data volumes were removed to ensure T1 equilibrium. Functional images were then accurately aligned with anatomical space using Sinc interpolation and FLIRT. Aligning functional and anatomical images with six degrees of freedom is essential for correcting any misalignments [ 25 ]. Normalization: The aligned images were normalized to the MNI152 3 mm template using FNIRT from the FSL suite, standardizing data from diverse sources into a uniform spatial framework. This process compensates for differences in spatial resolution and intensity that arise from various MRI scanners. Spatial Smoothing: To improve the signal-to-noise ratio, spatial smoothing was applied, aiming for a global full-width-at-half-maximum of 6 mm. This step strikes a balance between maintaining spatial resolution and minimizing image noise. Temporal Filtering: To filter out low-frequency drifts and high-frequency noise, a second-order band-pass filter with a range of 0.008–0.08 Hz was applied to the fMRI data [ 26 ]. Subject-Level Regression: Denoising was performed through subject-level regression against eight nuisance variables and their first derivatives, which included six rigid body motion parameters, as well as signals from ventricular cerebrospinal fluid and white matter. The FSL FAST method was used to extract these signals, ensuring that the resting-state fMRI data remained free from noise. Global Signal Regression: This step, embedded within the preprocessing pipeline, addresses variations arising from different acquisition sites. By correcting for discrepancies in acquisition parameters, it enhances the signal-to-noise ratio [ 27 ]. Nuisance Regressor Filtering: A consistent second-order Butterworth band-pass filter with a frequency range of 0.008–0.08 Hz was applied to all 17 nuisance regressors, ensuring uniformity across the dataset [ 28 ]. This standardized preprocessing approach enhances the reliability of comparisons between subjects and across studies. 2.4 Parcellation and Extraction of BOLD Time Series This study employed 333 cortical regions of interest (ROIs) from Gordon’s atlas [ 29 ], 26 cerebellar ROIs from the Diedrichsen atlas [ 31 ], 14 subcortical (SC) ROIs from the Harvard-Oxford (HO) atlas [ 30 ], along with a few smaller combined cerebellar ROIs. The selection of these atlases was based on previous studies in classifying and studying autistic brains [ 32 ]. A whole-brain mask was generated which covers the 95% of individuals BOLD signals detected in voxels. Subsequently, the voxel count within each ROI of the whole-brain mask was assessed. ROIs with a minimum of 95% of their voxels within the mask were included in the analysis [ 33 ]. This resulted in a total of 236 ROIs: 213 cortical, 9 cerebellar and 14 SC. The mean BOLD signal time series for each ROI was subsequently extracted. By averaging the signal across all voxels within each ROI at every time point, a representative time series was generated, reflecting the overall activity of the region. This approach effectively reduced the data's dimensionality while preserving the most relevant information for each region. 2.5 Time-frequency Spectrogram We applied the time-frequency methods such as STFT, CWT, MFC and SPWVD on fMRI BOLD time series signals and generated the spectrogram images. 2.5.1 Short-Time Fourier Transform STFT is a potent signal processing method used for analysing time-varying signals and extracting their frequency content. It divides the signal into shorter overlapping segments, applying Fourier transforms to capture frequency components. This forms the basis for creating spectrogram images, representing normalized, squared magnitude of STFT coefficients to depict dominant frequency information against time [ 9 ]. Mathematically this transform method is expressed as $$\:{X}_{stft}\left(\omega\:\right)={\int\:}_{-\infty\:}^{\infty\:}\:\:x\left(t\right)w\left(\tau\:-t\right){e}^{-j\omega\:t}dt$$ 1 where \(\:x\left(t\right)\) represents the signal, \(\:w\left(\tau\:-t\right)\) is a window function and \(\:\omega\:\) represents the frequency [ 34 ]. 2.5.2 Continuous Wavelet Transform CWT utilizes a wavelet function to create a scalogram, akin to a spectrogram, allowing for the analysis of both time and frequency domains. The scalograms produced by the CWT illustrate the frequency spectrum at each moment in time, accounting for the frequency content within a defined range determined by the wavelet's width [ 10 ] [ 8 ]. CWT of a signal x(t) is given by $$\:{X}_{cwt}\left(b\right)={\int\:}_{-\infty\:}^{\infty\:}\:\:x\left(t\right){\psi\:}_{a,b}^{*}\left(t\right)dt$$ 2 Where the function \(\:{\psi\:}_{a,b}^{*}\left(t\right)\) represents the complex conjugate of the mother wavelet ψ(t), which has been scaled by the parameter a and shifted by the parameter b. 2.5.3 Mel Frequency Cepstrum MFC spectrogram is produced by converting the signal's linear frequency of Mel-scale on a logarithmic scale using the STFT. This spectrum is then passed through a filter bank to determine the distribution of energy signal across the Mel-scale frequency range. Eigenvalues are subsequently computed to represent this energy distribution along the Mel-scale frequency spectrum [ 11 ]. Mathematically it is expressed as: $$\:{\left(Mel\:Cepstral\:Coefficient\right)\:c}_{i}=\sqrt{\frac{2}{L}}{\sum\:}_{m=1}^{L}\:\:lo{g}_{e}S\left(m\right)cos\left[\pi\:i\right(m-0.5\left)\right]$$ 3 Where \(\:L\) is the signal length and \(\:m\) is the Mel-scale frequency. 2.5.4 Smoothed Pseudo Wigner-Ville Distribution WVD serves as a method to examine the time-frequency properties of signals, providing a comprehensive view of signal behaviour in both time and frequency domains simultaneously. These spectrograms thus facilitate a deeper understanding of a signal's dynamic spectral characteristics, making them valuable tools in signal analysis [ 12 ]. It is mathematically expressed as $$\:{W}_{x(t,\nu\:)}={\int\:}_{-\infty\:}^{+\infty\:}\:\:{x}^{\:}(t+\frac{\tau\:}{2}){x}^{*}(t-\frac{\tau\:}{2}){e}^{-j2\pi\:\nu\:\tau\:}d\tau\:$$ 4 The primary issue encountered with the WVD is cross-term interference. To mitigate this interference, the SPWVD is commonly employed. It is a potent method for analyzing signal energy in both time and frequency domains, offering insights into higher harmonics and precise time-domain localization. This technique employs time and frequency windows to minimize interference from cross-terms [ 35 ]. The SPWVD is mathematically expressed as follows: $$\:{SW}_{g,h,X}(t,f)={\int\:}_{-\infty\:}^{\infty\:}\:\:{\int\:}_{-\infty\:}^{\infty\:}\:x(t+\frac{\tau\:}{2}){x}^{*}(t-\frac{\tau\:}{2})g\left(\nu\:\right)h\left(\tau\:\right){m\:e}^{-j2\pi\:f\tau\:}d\nu\:d\tau\:$$ 5 Where the function h(t) acts as a window to minimize cross-terms in the time domain, while g(t) serves as a window to reduce cross-terms in the frequency domain. 2.6 Feature Extraction We extracted GLCM, GLRLM, HM, ZM, FDTA, and FOS features from these spectrogram images. The GLCM utilizes second-order statistics to examine the texture by evaluating the relationships between pixels. This method typically involves analyzing pixel pairs to determine the frequency of specific combinations of brightness levels. Consequently, GLCM generates a matrix, with rows and columns corresponding to the gray values in the image, where each element denotes the frequency of specified pixel pairs [ 14 ] [ 36 – 38 ]. GLRLM stems from the observation that coarse textures tend to have longer gray-level runs, while fine textures consist mainly of shorter runs. It is denoted as p(i, j) , the matrix defines the number of runs with pixels of gray level i and run length j. From this matrix, different texture features can be extracted [ 13 ]. ZM serve as orthogonal descriptors that capture both global and geometric attributes of an image. The ZM of an image can be obtained by integrating the product of the image function and its corresponding Zernike polynomial over the unit circle. These polynomials are represented by equations defining radial and angular components. The amplitude of ZM remains invariant to rotation, making them useful for rotation-invariant feature extraction [ 16 ]. FDTA serves to discern various features within an image, such as its textural properties, surface roughness, smoothness, overall area, and solidity [ 39 ]. HM are computed to refine the matching process, unaffected by reflection, position, size, and orientation changes [ 17 ]. Table 2 Summary of Features Analysed in the Study Texture/Shape analysis Features GLCM (38) Contrast, Dissimilarity, Homogeneity, Energy (EN), Correlation, Angular Second Moment (ASM), Entropy, Mean, Variance, and Sum of Squares. The mean values and the range of values of the following features: 1) ASM, 2) Contrast, 3) Correlation, 4) Sum of Squares Variance (SSV), 5) Inverse Difference Moment (IDM), 6) Sum Average, 7) Sum Variance, 8) Sum Entropy (SE), 9) Entropy, 10) Difference Variance (DV), 11) Difference Entropy (DE), 12) Maximal Correlation Coefficient (MCC), 13) Information Measures of Correlation (IMC) GLRLM (5) Short Run Emphasis (SRE), Long Run Emphasis (LRE), Grey Level Uniformity (GLU), Run Length Uniformity (RLU), and Run Percentage (RPC) ZM (24) Moments 1 to 24 HM (7) Moments 1 to 7 FDTA (4) Hurst Coefficients (HC) 1 to 4 FOS (7) Mean, Variance, Skewness, Kurtosis, Energy, Entropy, and Coefficient of Variation (CV) 2.7 Feature Selection Feature selection is a vital component of classification tasks, aiding in speeding up learning processes by elimination of irrelevant features and enhancing accuracy. In this study, we utilized the RFECV method which selects features in a wrapper-style that iteratively identifies the most important subset of features by eliminating redundancy until attain the optimum number of features. Determining the ideal number of features is a critical hyper-parameter that needs careful tuning during training. This process is challenging because finding the right number of features to keep from the start can be complex. RFECV tackles this problem by using cross-validation to dynamically identify the optimal number of features. This approach improves classification performance by averaging the results across different validation folds [ 34 ] [ 40 ]. 2.8 Classification 2.8.1 Logistic Regression LR is a supervised learning algorithm used to estimate the probability of a categorical outcome based on multiple input features. It applies a logistic function to model the likelihood of a binary result. $$\:f\left(z\right)=\frac{1}{1+{e}^{-z}}$$ 6 Where \(\:z={b}_{0}+{b}_{1}{x}_{1}+{b}_{2}{x}_{2}+\cdots\:+{b}_{n}{x}_{n}\) , \(\:{x}_{1}\) to \(\:{x}_{n}\) denotes n attributes, while b to \(\:{b}_{n}\) represent weights [ 41 ] [ 33 ]. 2.8.2 Support Vector Machine SVM are used to separate data into different classes by using a hyperplane. When the data is not linearly separable in the original input space, SVM can apply nonlinear transformations to map the data into a higher-dimensional space. In SVM, each sample is represented as an m-dimensional vector and classified into two categories using an (m-1)-dimensional hyperplane. Out of all possible hyperplanes, the one that maximizes the margin which is the distance between the hyperplane and the closest data points from each class is chosen. This optimal hyperplane is essential for the performance of the SVM. The equation of the hyperplane in m-dimensional space is given by: $$\:y={W}_{0}+{W}_{1}{X}_{1}+{W}_{2}{X}_{2}+{W}_{3}{X}_{3}+\dots\:{W}_{m}{X}_{m}$$ 7 $$\:y={W}_{0}+\sum\:_{i=1}^{m}\:{W}_{i}{X}_{i}$$ 8 $$\:={W}_{0}+{W}^{T}X$$ 9 $$\:=b+{W}^{T}X$$ 10 where, w is the weight vector consisting of \(\:{W}_{1}\) , \(\:{W}_{2}\) , \(\:{W}_{3}\) ... \(\:{W}_{m}\) , b is the bias term and X is a vector of input variables, \(\:{X}_{1}\) , \(\:{X}_{2}\) , \(\:{X}_{3}\) ... \(\:{X}_{m}\) [ 42 ]. 2.8.3 Random Forest RF is a technique in ensemble learning that integrates multiple decision trees for both classification and regression tasks. It enhances the conventional bagging approach by introducing a layer of randomness. Unlike standard decision trees, in RF each node is divided based on a randomly chosen subset of predictors specific to that node, thereby mitigating overfitting while maintaining high predictive performance. Attribute selection in RF is guided by the Gini Index, which evaluates the impurity of a node and aids in determining the optimal split. $$\:\sum\:_{\:}\:\sum\:_{j\ne\:i}\:\frac{f({C}_{i},T)}{\left|T\right|}*\frac{f({C}_{j},T)}{\left|T\right|}$$ 11 where, \(\:{C}_{i}\) represents the class to which a randomly selected case, \(\:T\) denotes the training data, and \(\:\frac{f({C}_{i},T)}{\left|T\right|}\) signifies the likelihood that the selected sample is assigned to the class \(\:{C}_{i}\) [ 43 ]. 2.8.4 Extreme Gradient Boosting XGBoost is highly regarded for its scalability and outstanding performance while maintaining lower computational complexity. This gradient boosting classifier leverages decision trees to build a powerful prediction model by integrating several weak models into a single strong learner. The XGBoost algorithm trains multiple models in sequence, where each subsequent model aims to minimize the loss function of the overall system through gradient descent. This approach refines the model iteratively, enhancing the accuracy of predictions. The key idea behind XGBoost is to construct base learners that align with the negative gradient of the loss function [ 44 ] [ 45 ]. 2.8.5 Performance Evaluation We assessed the performance of classifiers using several metrics: accuracy, precision, sensitivity, F1-score, and the area under the receiver operating characteristic curve (ROC). Accuracy reflects the overall correctness of a model by counting the proportion of correct predictions across all categories. Sensitivity, also known as recall, measures effectiveness of the model in identifying the true positive instances, whereas specificity gauges its ability to correctly detect true negative cases. The F1-score combines precision and sensitivity into a single metric, offering a balanced view of the model's performance with respect to false positives and false negatives. The area under the curve (AUC) evaluates the model's ability to distinguish between classes by measuring the area under the ROC curve [ 34 ]. Table 3 List of performance metrics and their formula Performance metrices Formulae Accuracy \(\:\frac{TP+FP}{TP+FP+TN+FN}\) Sensitivity \(\:\frac{TP}{TP+FN}\) Specificity \(\:\frac{TN}{TN+FP}\) F1-score \(\:\frac{2*\left(Recall*Precision\right)}{Recall+Precision}\) AUC \(\:{\int\:}_{0}^{1}\:\:g\left(x\right)dx\) TP-True positive, FP- False positive, TN- True negative, FN- False negative, \(\:g\left(x\right)\) represents the receiver operating characteristic curve. 3. Results Figures 2 (a) and (b) show the average fMRI time series data for brain regions in individuals with ASD compared to TD subjects. The voxel intensity tends to be higher in the ASD group than in the TD group, though this difference does not occur consistently across all subjects and brain regions. Moreover, individuals with ASD display more irregular or less synchronized fluctuations in neural activity. These oscillations are well reflected in the respective time-frequency representation patterns shown in Figures (c-j). It can be observed that the signal consists of the lower frequency components which is clearly visible in the STFT as high intensity values in Figures (c) and (d). It reveals that the signal consists of more low frequency component compared to high frequency components. Furthermore, there are noticeable high fluctuations around 150 seconds in the ASD signal, which are depicted in the corresponding STFT spectrograms. In contrast, the TD group shows a more uniform intensity distribution in the STFT spectrograms. Similar patterns are observed in the spectrograms of CWT in Figures (e) and (f), MFC in Figures (g) and (h), and SPWVD in Figures (i) and (j). Figure 2. Representation of average time series BOLD fMRI signal of a brain region of (a) ASD, (b) TD, corresponding spectrograms using (c), (d) STFT, (e), (f) CWT, (g), (h) MFC and (i), (j) SPWVD. Figure 3 presents the classification results for the ROI that demonstrated the highest performance among the 236 ROIs analysed. The results were obtained using all 85 texture, shape, moment, FDTA, and FOS features extracted from the spectrograms with the LR, SVM, RF, and XGBoost classifiers. Figure 3 (a) illustrates the classification performance of the LR for all time-frequency methods, with CWT spectrograms achieving the highest accuracy of 73.57% for the network none in -34.7 35.6–9.6 coordinates. Figure 3 (b) displays the SVM performance across different time-frequency methods, where STFT achieved the highest accuracy of 76.09% for the network cingulo-opercular task control (COTC) in 6.7 5 55.9 coordinates. Figure 3 (c) represents the RF classifier's performance, with the MFC spectrograms attaining the highest accuracy of 78.92% for the network dorsal attention (DA) in 48.1 38.4 2.4 coordinates. Figure 3 (d) shows the classification performance of XGBoost, where the MFC spectrograms achieved the highest accuracy of 80.38% for the network somatosensory motor hand (SMH) in -5 -28.2 60.4 coordinates. It can be noted that the top performing spectrograms and corresponding networks are inconsistent between the classifiers. Notably, the XGBoost model consistently outperformed the LR, RF, and SVM classifiers across various spectrograms. The highest performance metrics for the XGBoost with MFC spectrograms achieved an accuracy of 80.38%, sensitivity of 77.77%, specificity of 82.85%, F1-score of 80.27%, and AUC of 80.31%, utilizing all 85 features. Figure 3. Classification performance comparison across time-frequency methods and classifiers considering all 85 features and their corresponding networks (a) LR, (b) SVM, (c) RF and (d) XGBoost Furthermore, we applied RFECV in our analysis to identify the optimal features for input to classifiers, aiming to enhance model performance. Figure 4 presents the classification results for the ROI that demonstrated the highest performance among the 236 ROIs analysed using only the optimal features selected from the 85 texture, shape, moment, FDTA, and FOS features. Figure 4 (a) illustrates the classification performance of the LR across all time-frequency methods, with SPWVD spectrograms achieving the highest accuracy of 86% using 5 distinct features optimized by RFECV for the network DA in 36.8 37.8 13.1 coordinates. Figure 4 (b) displays the SVM performance across different time-frequency methods, where MFC achieved the highest accuracy of 95.71% with the top 36 optimal features for the network fronto-parietal task control network (FPTC) in -5.5 29.3 44 coordinates. Figure 4 (c) represents the RF classifier's performance, with MFC spectrograms attaining the highest accuracy of 87.33% by using 25 optimal features for the network FPTC in 38.9 9.6 42.7 coordinates. Figure 4 (d) shows the classification performance of XGBoost, where MFC spectrograms achieved the highest accuracy of 85.9% with 26 optimal features for the network SMH in -5 -28.2 60.4 coordinates. It is notable that the top-performing spectrogram (MFC) is consistent between the SVM, RF, and XGBoost classifiers. However, number of features required for the top performing model and corresponding networks varied across the classifiers. The SVM model consistently outperformed the LR, RF, and XGBoost classifiers across various spectrograms. The highest performance metrics for the SVM with MFC spectrograms were an accuracy of 95.71%, sensitivity of 100%, specificity of 91.42%, F1-score of 95.76%, and AUC of 95.71%, utilizing 36 optimal features out of the 85 total features identified by RFECV. The findings demonstrate a significant improvement in performance when incorporating RFECV into our model. Figure 4. Classification performance comparison across time-frequency methods and classifiers using optimum features using RFECV and their corresponding networks (a) LR, (b) SVM, (c) RF and (d) XGBoost Figure 5 represents the ranking of the 36 optimal features identified by RFECV that contributed to the top-performing MFC-SVM model. Among these 36 features, GLCM, ZM, HM, GLRLM, FDTA and FOS contributed 15, 10, 5, 3, 2, and 1 feature respectively. It is evident that each feature group plays a role in the analysis. The most important feature is from the GLCM (homogeneity), followed by features from the FDTA (HC-3) and the ZM (radius-9-12) group. Notably, 36 out of the 85 features strike a balance, as the model's performance deteriorates when the number of features considered is either too low or too high. Figure 6 illustrates the region-wise performance of the MFC-SVM model using optimized features. Notably, the classification performance differed significantly across various brain regions and their associated networks. Certain regions exhibited superior classification performance, highlighting their greater relevance for analysis compared to considering all ROIs. This approach reduces computational costs and allows clinicians to focus on specific brain areas that have a greater impact on ASD. The highest performance accuracy was achieved for the FPTC (-5.5 29.3 44 coordinates) network at 95.71%, followed by 93.21% for none (-34.7 35.6–9.6 coordinates) and 88.76 for the COTC (36.7 5.2 12.7 coordinates) while the lowest was for the COTC (8.6 4.2 40.1 coordinates) network at 40.95%. This comprehensive analysis provides insights into the effectiveness and reliability of various time-frequency methods and classifiers across different brain regions, aiding informed decision-making in ASD diagnosis using neuroimaging. 4. Discussion This study explores the development of classification models such as LR, SVM, RF, and XGBoost for ASD, utilizing a combination of spectrogram time-frequency techniques such as STFT, MFC, CWT, and SPWVD, along with features like GLCM, FDTA, FOS, HM, GLRLM, and ZM extracted from 236 ROIs. We achieved accuracy of 80.38% and 95.71% using all features and optimum features by RFECV with 5-fold cross-validation approach. We found that FPTC network from − 5.5 29.3 44 coordinates produced the highest classification accuracy. Additionally, the top performing features are homogeneity, Hurst coefficient-3 and radius-9-12 from GLCM, FDTA and ZM group respectively. These findings could lead to future research on developing more sophisticated ASD classification systems. Such research might take a regional approach, focusing on various brain areas rather than individual subjects. Table 6 List of previous studies using time-frequency methods on fMRI BOLD signals for ASD diagnosis Study Database Sites (subjects) Atlas (Regions) Time frequency method Feature extraction Cross-validation Classifier Feature selection Performance (%) Network Our study ABIDE-I and ABIDE-II OHSU (36 ASD, 35 TD) Gordon's, HO, Diedrichsen (236) STFT, CWT, MFC, SPWVD GLCM, GLRLM, ZM, HM, FDTA and FOS 5-fold LR, SVM, RF, XGBoost RFECV Accuracy-95.71, sensitivity-100, specificity-91.42, F1-score-95.76, AUC-95.71 SMH, COTC, FPTC, DA, CPTC, SC, Visual, Auditory, Default [ 6 ] ABIDE-I and ABIDE-II OHSU (36 ASD, 35 TD) Gordon's, HO, Diedrichsen (236) CWT GLCM, GLRLM, ZM, HM, FDTA and FOS 5-fold CatBoost, DT - Accuracy − 83.04, Sensitivity − 66.66, Specificity- 85.57, F1 score − 75.85 RST [ 18 ] ABIDE - (41 ASD, 41 TD) AAL (116) PFT Googlenet, DenseNet201, Resnet18, and Resnet101 5-fold, 10-fold, 15-fold and 20-fold SVM, KNN - Accuracy- 96.7, Sensitivity- 96.6, Specificity- 96.9, Precision- 96.8 - [ 46 ] ABIDE SDSU, STANFORD, UM, KKI, LEUVEN, SBL, TRINITY, CALTECH, CMU, MAX, NYU, OHSU, OLIN; PITT, UCLA, USM, YALE, (505 ASD, 530 TD) AAL WC, PWC FC CNN 10-fold CNN - Accuracy- 95.2, Sensitivity- 96.7, Specificity- 94.3, Precision- 94.8 - [ 19 ] ABIDE CALTEC, CMU, KKI (41 ASD, 41 TD) AAL (116) CWT Googlenet, DenseNet201, Resnet18, and Resnet101 No cross-validation (Training-70%, Validation-15% and testing-15%) SVM, KNN - Accuracy- 85.9, Sensitivity- 79.3, Specificity- 92.6 - [ 47 ] ABIDE NYU, SBL, SDSU, TRINITY, YALE, USM, KKI, UM (36 ASD, 36 TD) AAL (116) WC CNN 5-fold, 10-fold, 15-fold, 20-fold, leave-one site validation CNN - Accuracy-89.8, Sensitivity- 90.1, Specificity − 89.7, Precision- 89.6, F1 score-9.8 - [ 4 ] NDAR - (50 ASD, 50 TD) HO CWT CNN 4-fold CNN - Accuracy-86, Sensitivity- 82, Specificity 92 CG, STG, PAC, AG [ 5 ] ABIDE YALE, PITT, UCLA, SDSU, NYU, TRINITY (222 ASD, 246 TD) HO (111) D3TDWT GARCH 5-fold SVM t-test Accuracy- 75.3 MTG, SG, PGR PFT-Progressive Fourier Transform, CALTECH-California Institute of Technology, CMU- Carnegie Mellon University, NYU-New York University, SBL-Social Brain lab, SDSU- San Diego State University, Trinity-Trinity College Institute of Neuroscience, YALE-Yale School of Medicine, USM-University of Utah School of Medicine, KKI-Kennedy Krieger Institute, UM-University of Michigan, D3TDWT-Double-Density Dual-Tree Discrete Wavelet Transform, GARCH-Generalized autoregressive conditional heteroscedasticity, AAL-Automated anatomical labeling, PITT- University of Pittsburgh School of Medicine, UCLA- University of California Los Angeles, STANFORD- Stanford University; UM-University of Michigan, LEUVEN-University of Leuven, MAX-Ludwig Maximilian University of Munich, OLIN-Olin Center; Institute of Living at Hartford Hospital, WC-Wavelet coherence, PWC-Principal wavelet coherence, MTG-Middle Temporal Gruys, SG-Supramarginal Gyrus, PGR-Paracingulate Gyrus R, CG-Cingulate gyri, STG-Superior temporal gyrus, PAC-Primary auditory cortex and AG-Angular gyrus, FPTC-Fronto-parietal task control network, CPTC- Cingulo Parietal Task Control 4.1. Effect of time-frequency methods In this study, BOLD time-series signals were analysed using four distinct time-frequency methods: STFT, CWT, MFC, and SPWVD, to generate spectrograms. These spectrograms served as the basis for feature extraction, which were then input into machine learning classifiers to evaluate model performance. Initially, the model demonstrated superior performance with MFC spectrograms, followed by STFT, SPWVD, and CWT, when utilizing all 85 features. However, upon employing RFECV for optimal feature selection, the model consistently outperformed with the MFC method, followed by CWT, STFT, and SPWVD. The adaptive nature of the MFC method, with its ability to provide a sparse representation focusing on low-frequency components, is useful for effectively capturing and highlighting the most relevant features of the BOLD signal, leading to improved performance of machine learning models in tasks such as ASD classification. This may also be attributed to the MFC spectrogram's generation process, which converts a signal's linear frequency scale to a logarithmic Mel scale using the STFT. This spectrum is then processed through a filter bank to determine the energy distribution across the Mel-scale frequency range. Eigenvalues are computed to represent this distribution, leading to improved performance of machine learning models. Our study demonstrates the superiority of MFC over traditional time-frequency methods like STFT, CWT, and SPWVD in analysing fMRI data [ 11 ]. Notably, previous studies have explored various methods, including CWT [ 6 ] [ 19 ] [ 4 ], PFT [ 18 ], WC [ 47 ], D3TDWT [ 5 ], and a combination of WC, PWC, and FC [ 46 ]. However, these studies did not conduct comparative analyses of distinct time-frequency methods, nor did they delve into the effects of STFT, MFC, and SPWVD in analysing BOLD time signals from fMRI. This comprehensive examination sheds light on the nuanced performance differences between these time-frequency methods and underscores the superiority of MFC spectrograms in ASD classification. 4.2. Impact of features In this study, we analysed a total of 85 features including texture and shape-based patterns. However, the optimal feature set for achieving the best accuracy with the MFC method and SVM classifier comprised 36 out of these 85 features. These features were categorized into groups such as GLCM, GLRLM, HM, ZM, FDTA, and FOS. Among these, the top-performing features were homogeneity from the GLCM group, the Hurst coefficient-3 from the FDTA group, and radius-9-12 from the ZM group. The specific features performed well due to their ability to capture essential characteristics of the BOLD signals. Homogeneity from the GLCM group reflects the similarity of pixel intensities, which is crucial for identifying consistent patterns in fMRI data [ 13 ]. The Hurst coefficient-3 from the FDTA group is indicative of the fractal nature of the time-series data, effectively capturing long-term patterns and self-similar structures [ 15 ]. The radius-9-12 feature from the ZM group provides a robust representation of image shapes and patterns, contributing to more accurate signal characterization [ 16 ]. In conclusion, the study highlights that a carefully selected subset of features significantly enhances the performance of machine learning models, with MFC-derived features demonstrating superior effectiveness in ASD classification. The number of selected features used for classification with respective time-frequency methods and classifiers, identified through the RFECV method for each region that performed better for different classifiers and corresponding time-frequency methods. Supplementary table 1 highlights the consistency of features among different time-frequency methods and classifiers. Notably, the highest contributing feature, ZM radius_9_2, consistently appeared 8 times in the analysis. Additionally, GLCM_MCC _Range, ZM radius_9_6, ZM radius_9_11, and FDTA HC_4 each contributed 7 times, among the total 85 features. However, studies never used these features in ASD classification using fMRI BOLD signals. 4.3. Impact of feature selection Our study examined effect of feature selection methods and classifiers in ASD classification. We employed two different approaches utilizing all available features and utilizing only the optimal subset of features identified through RFECV. When utilizing all 85 features for classification, the results demonstrated an accuracy of 80.38%, sensitivity of 77.77%, specificity of 82.85%, F1-score of 80.27%, and AUC of 80.31%. In contrast, the SVM classifier achieved the best performance when using the MFC spectrogram in combination with RFECV. It yielded an overall accuracy of 95.71%, sensitivity of 100%, specificity of 91.42%, F1-score of 95.76%, and AUC of 95.71%. This result was obtained using the top 36 important features. Before applying RFECV, the classification model's performance with all 85 features showed moderate accuracy and balanced sensitivity and specificity. However, including all features likely introduced noise and irrelevant data, reducing the model’s ability to detect key patterns crucial for ASD classification. After applying RFECV, performance improved significantly. By selecting the most relevant 36 features, RFECV filtered out redundant and irrelevant data, allowing the model to focus on the most informative aspects of the BOLD signals. This refined feature set led to significant improvements in accuracy, sensitivity, specificity, F1-score, and AUC. These results highlight the effectiveness of RFECV in enhancing model performance. Further, RFECV improves performance by systematically evaluating the contribution of each feature and recursively removing the least significant ones. This process helps in reducing overfitting by eliminating noise and redundant features, enhancing computational efficiency with fewer features leading to faster training and prediction times, and improving model interpretability as a smaller set of relevant features makes the model easier to interpret and understand [ 40 ]. Studies have shown that optimal feature selection enhances the accuracy and robustness of machine learning models across various applications, including medical diagnostics, image processing, and signal analysis [ 34 ]. This study's findings show that using RFECV for optimal feature selection can significantly improve the accuracy and efficiency of ASD classification models. This approach not only improves the overall performance metrics but also contributes to a more streamlined and interpretable model, facilitating better clinical and research applications. 4.4. Effect of Classifiers Across various time-frequency methods, we observed notable variations in classification performance. MFC stood out as particularly effective, achieving an impressive accuracy of 80.38% using XGBoost classifier. Similarly, the STFT method performed commendably with an accuracy of 78.85% using XGBoost classifier. Conversely, the CWT showed noteworthy accuracy of 75.89% using SVM, and the SPWVD method demonstrated respectable accuracy, reaching 76.25% using XGBoost classifier. However, the application of RFECV for feature selection resulted in significant improvements in classification accuracy across diverse time-frequency methods, classifiers, and associated brain networks. Notably, the highest accuracies were achieved with STFT yielding 88.76% accuracy using SVM classifier, CWT achieving 93.21% using SVM, MFC obtaining 95.71% using SVM, and SPWVD reaching 86% using LR classifier. Among the classifiers tested, the SVM consistently outperformed others in processing BOLD signals. The superior performance of SVM can be attributed to its capability to effectively manage complex data and determine the optimal boundary for distinguishing between different groups [ 42 ]. This is particularly beneficial in analysing complex fMRI data where the distinction between ASD and TD patterns may be subtle and multidimensional. While previous studies have achieved high classification accuracy through the use of intricate deep learning algorithms for feature extraction, their analyses often lack network-based approaches. For instance, [ 18 ] achieved commendable results but did not incorporate network-based methods. Similarly, although a few studies have conducted region-wise analyses, such as those by [ 4 – 6 ], our model's performance surpasses these prior studies. Specifically, [ 5 ] utilized statistical t-tests for feature selection, yet our model's performance exceeds. This superior performance can be partly attributed to our use of a homogeneous and balanced dataset, derived from a single site, which minimizes variability and enhances the reliability of our findings. In conclusion, this study's findings demonstrate that integrating RFECV for optimal feature selection and utilizing SVM classifiers notably improves the accuracy of ASD classification models. This approach not only improves overall performance metrics but also offers a more refined and interpretable model, which is crucial for advancing diagnostic accuracy and treatment strategies in ASD research. 4.5. Region-based analysis and clinical implications Our analysis of 236 brain regions provides a foundation for future investigations into key contributors to ASD diagnosis. Previous studies using region-based approaches have often yielded inconsistent findings [ 4 – 6 ]. In our study, we identified several influential networks and their respective pipelines: COTC (STFT-LR, STFT-SVM, STFT-RF, CWT-RF), SMH (MFC-XGBoost), FPTC (CWT-XGBoost, MFC-SVM), DA (SPWVD-LR), CPTC (SPWVD-RF), None (STFT-XGB, CWT-LR, SPWVD-SVM), Visual (CWT-SVM), Auditory (SPWVD-XGBoost), and Default (STFT-RF), utilizing all 85 features. Following RFECV, the networks that remained influential were COTC (STFT-SVM, CWT-RF), SMH (MFC-XGBoost), FPTC (MFC-SVM), DA (SPWVD-LR), CPTC (SPWVD-RF), SC (SPWVD-SVM), Visual (STFT-LR), Auditory (SPWVD-XGBoost), None (CWT-LR, CWT-SVM, CWT-XGB, MFC-LR) and Default (STFT-RF). Previous research has highlighted the involvement of various networks such as COTC, Default [ 33 ], RST, VA, FPTC, and Visual [ 33 ] [ 6 ], CG, STG, PAC, AG [ 4 ], MTG, SG, PGR [ 5 ]. The networks identified in our study primarily involve cortical regions (COTC, Default, FPTC, SMH, DA, CPTC, Visual, Auditory) and SCregion. Research has identified associations in ASD with smaller SC volumes in the pallidum, putamen, amygdala, and nucleus accumbens, along with increased cortical thickness in the frontal cortex and reduced thickness in the temporal cortex. Age-related analyses reveal altered cortical thickness development in ASD, with notable differences emerging around adolescence. Notably, no age-by-ASD interactions were found in SC regions. These findings deepen our understanding of ASD’s neurobiological basis, highlighting both structural differences and developmental patterns in affected individuals [ 48 ]. 4.6. Effect of process pipeline In this study, we evaluated the impact of different process pipelines on ASD classification performance by analyzing four time-frequency methods (STFT, CWT, MFC, and SPWVD), four classifiers (LR, XGBoost, RF, and SVM), 236 brain regions, and two feature selection approaches: using all 85 features and using the optimal feature subset identified through RFECV. Among the tested pipelines, the highest performance was achieved by the MFC-XGBoost pipeline using all 85 features for the SMH region [ 49 ] and the MFC-SVM pipeline using the optimal features selected by RFECV for the FPTC region [ 50 ]. The MFC-XGBoost pipeline performed well due to XGBoost robust gradient boosting framework, which excels in handling structured data and preventing overfitting through regularization techniques. The combination of MFC's ability to capture sparse and low-frequency features of the BOLD signals with XGBoost powerful classification capability enabled this pipeline to effectively distinguish between ASD and TD subjects [ 45 ]. Similarly, the MFC-SVM pipeline achieved high performance when using the optimal features selected by RFECV. SVM is known for its effectiveness in high-dimensional spaces, which makes it well-suited for analysing fMRI data [ 42 ]. The use of MFC provided a detailed representation of the signal characteristics, while RFECV ensured that only the most relevant features were used, thereby improving the model's performance [ 11 ]. Previous studies have shown that incorporating advanced algorithms like XGBoost and SVM, along with effective feature selection techniques, can significantly improve the accuracy of medical diagnostic models [ 19 ] [ 18 ] [ 5 ]. In conclusion, the findings of this study underscore the importance of a well-designed process pipeline in improving ASD classification accuracy. These pipelines leveraged the strengths of their respective classifiers and the detailed feature representation provided by MFC, resulting in superior classification performance. This study highlights the potential of combining advanced feature extraction, selection methods, robust classifiers and specific network to enhance diagnostic accuracy and contribute to more effective ASD research and clinical applications. 4.7. Limitations and future scope Our study highlights the significant potential of MFC spectrograms followed by CWT, STFT and SPWVD spectrograms for identifying biomarkers for diagnosing ASD. However, several limitations must be addressed before this method can be applied in clinical settings. First, the method needs to be validated on a larger dataset and with a comprehensive classification model to confirm its robustness and generalizability. Our research exclusively employed machine learning classifiers without incorporating deep learning techniques. Deep learning models, although more data and resource-intensive, could potentially enhance clinical diagnosis accuracy. The current approach is limited by a small sample size, including only 36 individuals with ASD and 35 TD individuals. This limited sample necessitates validation on larger and more diverse datasets. Moreover, our study did not classify all sites as previous works have done, which could affect the generalization of our findings. Future research should explore lightweight deep learning models to enhance diagnostic accuracy while addressing the computational constraints common in healthcare settings. These models could offer more refined insights despite data and computational challenges. Crucial next steps include conducting longitudinal studies and applying our methodology to diverse datasets. This approach will enable us to track the progression of ASD over time and validate our findings across diverse demographic groups and clinical profiles. By examining neurodevelopmental trajectories in ASD and extending these methods to other neurodevelopmental disorders, we can achieve a more comprehensive understanding of these conditions. Additionally, efforts should prioritize enhancing the accessibility and practicality of advanced neuroimaging techniques in clinical practice. Incorporating these methods into routine diagnostic procedures requires addressing logistical challenges to ensure their widespread adoption and usefulness. This integration will be essential for enhancing diagnostic precision and optimizing treatment planning for ASD. 5. Conclusion Through this study, we explored the potential of using different time-frequency methods to analyse BOLD time-series signals from fMRI Data for ASD Classification. We employed four distinct methods: STFT, CWT, MFC, and SPWVD to generate spectrograms. These spectrograms were then used to extract various features, including GLCM, GLRLM, FDTA, HM, ZM, and FOS, which were input into machine learning classifiers LR, SVM, RF and XGBoost to evaluate their performance. Our findings revealed that MFC spectrograms consistently exhibited the highest performance, achieving an accuracy of 80.38% when all 85 features were used with XGBoost and 95.71% when optimal features were selected using RFECV and SVM. Comparative analyses with previous studies indicate that while various methods have been employed to classify ASD, our approach stands out due to its comprehensive comparative analysis of distinct time-frequency methods and the integration of optimal feature selection strategies. Prior research often lacked network-based analyses and did not explore the combined effects of STFT, MFC, and SPWVD in detail. Our study bridges this gap, offering valuable insights into the effectiveness of various time-frequency methods and highlighting the crucial role of feature selection. Moreover, our analysis included an extensive region-based approach, identifying specific brain networks such as the Visual, COTC, Default, None, FPTC, SMH, DA, SC, CPTC, Auditory as significantly contributing to the classification accuracy. These findings suggest that future research should focus on these networks for improved diagnostic precision. In conclusion, this study demonstrates the effectiveness of using spectrograms and optimal feature selection techniques in accurately classifying ASD. These promising results underscore the potential of these methods for early diagnosis and intervention in clinical settings. They pave the way for more refined and reliable diagnostic tools for ASD. Declarations Conflict of interest: The authors have no relevant financial or non-financial interests to disclose. Ethics approval: The data used in the study from the publicly available ABIDE database. Data availability statement: The data used for this study was obtained from the publicly available ABIDE database https://fcon_1000.projects.nitrc.org/indi/abide/. Funding statement: This research has received support from the Indian Council of Medical Research (ICMR), reference number R&D/SA/ICMR/BME/24-25/02/588. Acknowledgement: The authors also acknowledge the PARAM Shivay supercomputer facility at IIT BHU, Varanasi, India, for their valuable assistance during this study. References L. Borràs-Ferrís, Ú. Pérez-Ramírez, and D. Moratal, “Link-Level Functional Connectivity Neuroalterations in Autism Spectrum Disorder: A Developmental Resting-State fMRI Study.,” Diagnostics (Basel) , vol. 9, no. 1, Mar. 2019, doi: 10.3390/diagnostics9010032. S. Raj and S. 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Espitia, “EEG signal analysis using classification techniques: Logistic regression, artificial neural networks, support vector machines, and convolutional neural networks.,” Heliyon , vol. 7, no. 6, p. e07258, Jun. 2021, doi: 10.1016/j.heliyon.2021.e07258. G. Manoj et al. , “Diagnostic classification of autism spectrum disorder using sMRI improves with the morphological distance-related features compared to morphological features,” Res. Sq. , Nov. 2022, doi: 10.21203/rs.3.rs-2277683/v1. L. Breiman, “Random Forests,” Springer Science and Business Media LLC , vol. 45, pp. 5–32, 2001, doi: 10.1023/a:1010933404324. T. Chen and C. Guestrin, “XGBoost: A Scalable Tree Boosting System,” in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD ’16 , New York, New York, USA, Aug. 2016, pp. 785–794, doi: 10.1145/2939672.2939785. W. Zhu, S. Shen, and Z. Zhang, “Improved multiclassification of schizophrenia based on xgboost and information fusion for small datasets.,” Comput. Math. Methods Med. , vol. 2022, p. 1581958, Jul. 2022, doi: 10.1155/2022/1581958. M. I. Al-Hiyali, N. Yahya, I. Faye, M. S. Al-Quraishi, and A. Al-Ezzi, “Principal subspace of dynamic functional connectivity for diagnosis of autism spectrum disorder,” Appl. Sci. , vol. 12, no. 18, p. 9339, Sep. 2022, doi: 10.3390/app12189339. M. I. Al-Hiyali, N. Yahya, I. Faye, and A. F. Hussein, “Identification of autism subtypes based on wavelet coherence of BOLD FMRI signals using convolutional neural network.,” Sensors , vol. 21, no. 16, Aug. 2021, doi: 10.3390/s21165256. D. van Rooij et al. , “Cortical and subcortical brain morphometry differences between patients with autism spectrum disorder and healthy individuals across the lifespan: results from the ENIGMA ASD working group.,” Am. J. Psychiatry , vol. 175, no. 4, pp. 359–369, Apr. 2018, doi: 10.1176/appi.ajp.2017.17010100. S. Khan et al. , “Somatosensory cortex functional connectivity abnormalities in autism show opposite trends, depending on direction and spatial scale.,” Brain , vol. 138, no. Pt 5, pp. 1394–1409, May 2015, doi: 10.1093/brain/awv043. V. Yuk, C. Urbain, E. Anagnostou, and M. J. Taylor, “Frontoparietal Network Connectivity During an N-Back Task in Adults With Autism Spectrum Disorder.,” Front. Psychiatry , vol. 11, p. 551808, Sep. 2020, doi: 10.3389/fpsyt.2020.551808. Supplementary Table 1 Supplementary Table 1 is not available with this version Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5170177","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":362078190,"identity":"822de37d-e2c8-40ad-8e8b-83072ef734c2","order_by":0,"name":"Tikaram Tikaram","email":"","orcid":"","institution":"Indian Institute of Technology (BHU)","correspondingAuthor":false,"prefix":"","firstName":"Tikaram","middleName":"","lastName":"Tikaram","suffix":""},{"id":362078191,"identity":"4d6bb80c-34d7-4795-8c05-fdc6efdd0853","order_by":1,"name":"Utkarsh Raj","email":"","orcid":"","institution":"Indian Institute of Technology (BHU)","correspondingAuthor":false,"prefix":"","firstName":"Utkarsh","middleName":"","lastName":"Raj","suffix":""},{"id":362078192,"identity":"65bd31b8-9bf6-4032-9231-3a530645e49b","order_by":2,"name":"Ravi Ratnaik","email":"","orcid":"","institution":"Indian Institute of Technology (BHU)","correspondingAuthor":false,"prefix":"","firstName":"Ravi","middleName":"","lastName":"Ratnaik","suffix":""},{"id":362078193,"identity":"439ea4c7-faa2-40d0-adba-072607f9cef5","order_by":3,"name":"Jac Fredo Agastinose Ronickom","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIie3RsQqCQBjA8e+41XCtRV/hRGjpZU6CWhzyCTIEXQJXpccIxFH4Bpd7gMAlEJpawhforiKaTseG+w8fcvqDTw7AZPrDSAxUDbApial6UDWTyCIhh2QSkb0Ja4B8if77DHtG6srxW5r1UY1gZw3BnW6x48bnRHT+EuVipUCYCw5YaP8lpA1Ju6BSZJYiwAUALR3J7y+yPycf4o6SIqRcEs7oh7BxcvNZIDqvkIudynRreSKItcTL1/38UXeunbfXIUpXjtMiDloSy8F/DqzX9epytW9NJpPJpHoCOpBRYzmh4WoAAAAASUVORK5CYII=","orcid":"","institution":"Indian Institute of Technology (BHU)","correspondingAuthor":true,"prefix":"","firstName":"Jac","middleName":"Fredo Agastinose","lastName":"Ronickom","suffix":""}],"badges":[],"createdAt":"2024-09-28 11:38:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5170177/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5170177/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68886643,"identity":"0a858565-8407-4f85-8838-7f552b212e57","added_by":"auto","created_at":"2024-11-13 06:44:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1545214,"visible":true,"origin":"","legend":"\u003cp\u003eImplementation pipeline for the proposed study\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/618eacbbb2ef9604850f922d.png"},{"id":68885307,"identity":"da5f4b14-3bdc-4e93-8712-83f8c059f593","added_by":"auto","created_at":"2024-11-13 06:36:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":2374380,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentation of average time series BOLD fMRI signal of a brain region of (a) ASD, (b) TD, corresponding spectrograms using (c), (d) STFT, (e), (f) CWT, (g), (h) MFC and (i), (j) SPWVD.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/d4b933aa91d87466d01f56de.png"},{"id":68886642,"identity":"68df4cbc-59cb-436d-9526-9885f3186ae8","added_by":"auto","created_at":"2024-11-13 06:44:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":645748,"visible":true,"origin":"","legend":"\u003cp\u003eClassification performance comparison across time-frequency methods and classifiers considering all 85 features and their corresponding networks (a) LR, (b) SVM, (c) RF and (d) XGBoost\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/55c87c04060b34147085dd4a.png"},{"id":68885305,"identity":"65c6b673-abe8-4dc9-a91a-6e4c04e10bdd","added_by":"auto","created_at":"2024-11-13 06:36:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":499660,"visible":true,"origin":"","legend":"\u003cp\u003eClassification performance comparison across time-frequency methods and classifiers using optimum features using RFECV and their corresponding networks (a) LR, (b) SVM, (c) RF and (d) XGBoost\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/99e80bf5a4153574709b6be3.png"},{"id":68886644,"identity":"33143afd-336e-4ecd-a911-f85c2eed3c2b","added_by":"auto","created_at":"2024-11-13 06:44:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":360838,"visible":true,"origin":"","legend":"\u003cp\u003eFeature ranking of the 36 optimal features identified by RFECV which contributed to the top performing model MFC-SVM (FPTC).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/e35c35066ef217d551760f65.png"},{"id":68885302,"identity":"6cc569af-6eab-4cd8-98fa-76db8bda84dd","added_by":"auto","created_at":"2024-11-13 06:36:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":276812,"visible":true,"origin":"","legend":"\u003cp\u003eAverage 5-fold classification performance for all 236 regions using MFC-SVM\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/51a7ab92c22e997813b07234.png"},{"id":78866079,"identity":"5476b136-6b91-4523-8649-429d09b728ea","added_by":"auto","created_at":"2025-03-20 04:01:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9075009,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5170177/v1/bb0c4f79-b71b-4cfc-a2b2-d3c711b1deb1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Advancing ASD diagnostic classification using time-frequency spectrograms of fMRI BOLD signals and machine learning","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAutism spectrum disorder (ASD) is a persistent neurodevelopmental condition beginning in childhood, characterized by key impairments in social interaction, communication, and repetitive behaviours. These challenges are often linked to deficits in executive functions such as working memory, inhibition, cognitive flexibility, and planning. Affecting about 1 in 100 children worldwide, ASD requires customized therapeutic approaches due to its diverse manifestations and the lack of a definitive cure [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Early detection and intervention are crucial for alleviating symptoms and improving the quality of life for individuals with ASD. Diagnosis typically involves observation and input from parents, educators, and medical professionals, including pediatricians, child psychologists, neurologists, and therapists. Diagnosing ASD in adults is more challenging compared to older children and adolescents, due to symptom overlap with other mental health conditions. Although behavioural signs can appear as early as 6 months of age, the diagnostic process is complex, often leading to delays of several months to years because of the wide range of behaviours and subjective symptoms associated with ASD. Thus, there is a significant need for research into autism-specific brain imaging biomarkers to aid in early ASD detection [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMagnetic resonance imaging (MRI) is an essential tool for examining structural brain changes in children with ASD. Functional MRI (fMRI), specifically, has been extensively used to study overall brain function. These sophisticated imaging techniques can detect subtle alterations in brain metabolism and connectivity within neural networks over time, whether during cognitive tasks or resting-state brain activity. Blood-oxygen-level-dependent (BOLD) fMRI, which monitors changes in deoxyhemoglobin concentration, enables the visualization of neural metabolic changes linked to both cognitive tasks and spontaneous brain activity. In this study, we used resting-state fMRI data to find specific brain imaging biomarkers associated with ASD.\u003c/p\u003e \u003cp\u003eIdentifying distinct neural networks associated with ASD is crucial for uncovering biomarkers that can facilitate early and precise diagnosis. Numerous studies have attempted to pinpoint the brain networks affected in individuals with ASD. For instance, [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] highlighted the involvement of the cingulate gyri, superior temporal gyrus, and primary auditory cortex in ASD. Meanwhile, [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] observed variations in the angular gyrus, middle temporal gyrus, supramarginal gyrus, and paracingulate gyrus. Additionally, [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] determined that the retrosplenial temporal network provided the most reliable performance in ASD diagnostic classification. However, the specific brain regions or networks implicated in ASD have varied across studies. In our research, we have analysed a broad spectrum of brain regions across different networks to further explore the neurobiological mechanisms underlying ASD.\u003c/p\u003e \u003cp\u003eFunctional connectivity (FC) is the traditional approach for analysing fMRI signals, focusing on the temporal correlation of BOLD signals between distinct brain regions. Nonetheless, the BOLD signal is influenced by a range of physiological processes, including neuronal activity, metabolic functions, cardiac cycles, and levels of alertness, in addition to factors associated with imaging equipment and individual differences among participants. These influences introduce noise, which can compromise the accuracy of FC analysis results [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Conversely, time-frequency methods break down signals in both the time and frequency domains, offering a more detailed perspective on signal behaviour in these domains simultaneously. Various time-frequency techniques, such as short-time Fourier transform (STFT), continuous wavelet transforms (CWT), discrete wavelet transform (DWT), Mel frequency cepstrum (MFC), Wigner-Ville distribution (WVD), smoothed pseudo Wigner-Ville distribution (SPWVD), Gabor-Wigner transform, Hilbert\u0026ndash;Huang transform, and bilinear time-frequency distribution, have been employed for different applications [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The STFT operates similar to the Fourier transform but incorporates a window function and short wavelets localized in both time and frequency, using overlapping fixed-sized windows to calculate multiple traditional Fourier transforms [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The CWT addresses the limitations of the STFT by forgoing a window function and instead employing a family of base functions that adjust with frequency, thereby providing high resolution across the full frequency spectrum [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. MFC spectrograms are created by converting the signal's linear frequency scale into a logarithmic Mel scale using STFT, followed by filtering through a filter bank to assess signal energy distribution across the Mel scale frequency range. The WVD offers a more concentrated energy representation of the signal compared to the STFT [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. However, WVD is prone to cross-term interference, complicating the interpretation of its time-frequency representation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. To reduce this interference, the SPWVD is often used. This method is effective in analysing signal energy across time and frequency domains, offering insights into higher harmonics and precise localization in the time domain [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In this study, we compare the effectiveness of the STFT, CWT, MFC, and SPWVD methods in analysing fMRI BOLD signals for the diagnostic classification of ASD subjects.\u003c/p\u003e \u003cp\u003eExtracting texture and moment-based features from spectrograms is vital for identifying specific patterns in fMRI BOLD signals associated with ASD. Commonly used techniques for quantifying texture information within images include the gray-level co-occurrence matrix (GLCM) and gray-level run-length matrix (GLRLM). GLCM examines the spatial relationships between pairs of pixels, while GLRLM assesses the length and orientation of sequences of contiguous pixels that share the same gray level. In addition, feature extraction from 2D signal representations involves methods such as fractal dimension texture analysis (FDTA), Zernike's moments (ZM), Hu's moments (HM), and first-order statistics (FOS). FDTA is especially effective for texture analysis as it evaluates the complexity and irregularity of patterns. ZM and HM are used to capture global and local shape characteristics within images, respectively. FOS involves metrics such as mean, variance, skewness, and kurtosis, which are often applied in extracting features from biological signals in biomedical research. In this study, we explored the use of features derived from spectrograms, including GLCM, GLRLM, HM, ZM, FDTA, and FOS, to aid in diagnosing ASD.\u003c/p\u003e \u003cp\u003eArtificial intelligence, specifically through machine learning and deep learning techniques, is highly effective at handling complex, high-dimensional data and identifying underlying patterns in features to automate ASD diagnosis. A variety of machine learning approaches ranging from linear to non-linear models, as well as tree-based and ensemble methods have been widely applied in ASD diagnosis. Previous studies have employed machine learning classifiers including k-nearest neighbours (KNN) [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], support vector machines (SVM) [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], decision trees, and categorical boosting [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], along with deep learning techniques [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] for classifying ASD. However, implementing deep learning algorithms often requires a large dataset and computationally powerful hardware. In this study, we utilized logistic regression (LR), extreme gradient boosting (XGBoost), SVM, and random forest (RF) for the diagnostic classification of ASD.\u003c/p\u003e \u003cp\u003eThe main contributions of this manuscript are\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eExamined a large number of brain regions and networks to identify the neurobiological correlates of ASD.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAnalysed the effect of four different time-frequency methods STFT, CWT, MFC, and SPWVD in extracting patterns from fMRI BOLD signals\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eEvaluated the impact of various texture features GLCM, GLRLM, FDTA, HM, ZM, and FOS in identifying patterns from the time-frequency spectrograms\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eImplemented machine learning algorithms, such as LR, XGBoost, SVM and RF to automate the process of ASD diagnosis\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Process pipeline\u003c/h2\u003e \u003cp\u003eThe pipeline used in this study is demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The evaluation pipeline included (1) Preprocessing the fMRI data, (2) Parcellation of brain regions and extraction of BOLD signal, (3) Generate spectrograms using time-frequency methods, (4) Feature extraction, and (5) Feature selection was performed incorporating recursive feature elimination combined with cross-validation (RFECV) and classification using machine learning algorithms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Dataset\u003c/h2\u003e \u003cp\u003eIn this research, we acquired fMRI data from the open-access Autism Brain Imaging Data Exchange (ABIDE-I \u0026amp; ABIDE-II) datasets. It contains numerous resting-state fMRI, sMRI, and DTI of ASD as well as typically developing (TD) gathered from multiple global sites, with authorization of local institutional review boards [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. This analysis focused on resting-state fMRI data from subjects with their eyes open, as the BOLD signals are influenced by the state of the eyes [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Further, images with at least 80% of original volumes retained after filtering, and root mean square deviation (motion) less than 0.2 were included in the analysis to avoid head movement effects on BOLD fluctuations [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. We recorded participant diagnostic state, gender and age based on the demographic information mentioned in the dataset description. The age range of our participants were 7\u0026ndash;15 years and 8\u0026ndash;14 years old for ASD and TD respectively. 30 males, and 6 females subjects with ASD and 22 males and 13 females with TD individuals were included in our study from Oregon Health and Science University (OHSU) site. Demographic information of subjects considered in this study is summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDemographic information\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eASD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTD\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of subjects\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge in years (range)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.57\u0026thinsp;\u0026plusmn;\u0026thinsp;2.65 (7\u0026ndash;15)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.57\u0026thinsp;\u0026plusmn;\u0026thinsp;2.65 (8\u0026ndash;14)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender ratio (M/F)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30/6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e22/13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHandedness (R/L/M)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35/0/1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35/0/0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFIQ/VIQ/PIQ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e106.19\u0026thinsp;\u0026plusmn;\u0026thinsp;16.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e118.45\u0026thinsp;\u0026plusmn;\u0026thinsp;12.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eM-Males, F-Females, R-Right, L-Left, M- Mixed handed, FIQ: Full Scale Intelligence Quotient, VIQ: Verbal Intelligent Quotient, PIQ: Performance Intelligence Quotient.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Preprocessing\u003c/h2\u003e \u003cp\u003eResting-state fMRI data were preprocessed using the functional neuroimaging tools AFNI [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] and FSL 5.0 [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The preprocessing techniques in this study comprised seven key steps to improve the quality of the data. These steps are as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTrimming and Alignment: To start, initially fMRI data volumes were removed to ensure T1 equilibrium. Functional images were then accurately aligned with anatomical space using Sinc interpolation and FLIRT. Aligning functional and anatomical images with six degrees of freedom is essential for correcting any misalignments [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eNormalization: The aligned images were normalized to the MNI152 3 mm template using FNIRT from the FSL suite, standardizing data from diverse sources into a uniform spatial framework. This process compensates for differences in spatial resolution and intensity that arise from various MRI scanners.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSpatial Smoothing: To improve the signal-to-noise ratio, spatial smoothing was applied, aiming for a global full-width-at-half-maximum of 6 mm. This step strikes a balance between maintaining spatial resolution and minimizing image noise.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTemporal Filtering: To filter out low-frequency drifts and high-frequency noise, a second-order band-pass filter with a range of 0.008\u0026ndash;0.08 Hz was applied to the fMRI data [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSubject-Level Regression: Denoising was performed through subject-level regression against eight nuisance variables and their first derivatives, which included six rigid body motion parameters, as well as signals from ventricular cerebrospinal fluid and white matter. The FSL FAST method was used to extract these signals, ensuring that the resting-state fMRI data remained free from noise.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eGlobal Signal Regression: This step, embedded within the preprocessing pipeline, addresses variations arising from different acquisition sites. By correcting for discrepancies in acquisition parameters, it enhances the signal-to-noise ratio [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eNuisance Regressor Filtering: A consistent second-order Butterworth band-pass filter with a frequency range of 0.008\u0026ndash;0.08 Hz was applied to all 17 nuisance regressors, ensuring uniformity across the dataset [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. This standardized preprocessing approach enhances the reliability of comparisons between subjects and across studies.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Parcellation and Extraction of BOLD Time Series\u003c/h2\u003e \u003cp\u003eThis study employed 333 cortical regions of interest (ROIs) from Gordon\u0026rsquo;s atlas [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], 26 cerebellar ROIs from the Diedrichsen atlas [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], 14 subcortical (SC) ROIs from the Harvard-Oxford (HO) atlas [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], along with a few smaller combined cerebellar ROIs. The selection of these atlases was based on previous studies in classifying and studying autistic brains [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. A whole-brain mask was generated which covers the 95% of individuals BOLD signals detected in voxels. Subsequently, the voxel count within each ROI of the whole-brain mask was assessed. ROIs with a minimum of 95% of their voxels within the mask were included in the analysis [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. This resulted in a total of 236 ROIs: 213 cortical, 9 cerebellar and 14 SC. The mean BOLD signal time series for each ROI was subsequently extracted. By averaging the signal across all voxels within each ROI at every time point, a representative time series was generated, reflecting the overall activity of the region. This approach effectively reduced the data's dimensionality while preserving the most relevant information for each region.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Time-frequency Spectrogram\u003c/h2\u003e \u003cp\u003eWe applied the time-frequency methods such as STFT, CWT, MFC and SPWVD on fMRI BOLD time series signals and generated the spectrogram images.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.5.1 Short-Time Fourier Transform\u003c/h2\u003e \u003cp\u003eSTFT is a potent signal processing method used for analysing time-varying signals and extracting their frequency content. It divides the signal into shorter overlapping segments, applying Fourier transforms to capture frequency components. This forms the basis for creating spectrogram images, representing normalized, squared magnitude of STFT coefficients to depict dominant frequency information against time [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Mathematically this transform method is expressed as\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{X}_{stft}\\left(\\omega\\:\\right)={\\int\\:}_{-\\infty\\:}^{\\infty\\:}\\:\\:x\\left(t\\right)w\\left(\\tau\\:-t\\right){e}^{-j\\omega\\:t}dt$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the signal, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:w\\left(\\tau\\:-t\\right)\\)\u003c/span\u003e\u003c/span\u003e is a window function and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\omega\\:\\)\u003c/span\u003e\u003c/span\u003e represents the frequency [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.5.2 Continuous Wavelet Transform\u003c/h2\u003e \u003cp\u003eCWT utilizes a wavelet function to create a scalogram, akin to a spectrogram, allowing for the analysis of both time and frequency domains. The scalograms produced by the CWT illustrate the frequency spectrum at each moment in time, accounting for the frequency content within a defined range determined by the wavelet's width [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. CWT of a signal x(t) is given by\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{X}_{cwt}\\left(b\\right)={\\int\\:}_{-\\infty\\:}^{\\infty\\:}\\:\\:x\\left(t\\right){\\psi\\:}_{a,b}^{*}\\left(t\\right)dt$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere the function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\psi\\:}_{a,b}^{*}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the complex conjugate of the mother wavelet ψ(t), which has been scaled by the parameter a and shifted by the parameter b.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.5.3 Mel Frequency Cepstrum\u003c/h2\u003e \u003cp\u003eMFC spectrogram is produced by converting the signal's linear frequency of Mel-scale on a logarithmic scale using the STFT. This spectrum is then passed through a filter bank to determine the distribution of energy signal across the Mel-scale frequency range. Eigenvalues are subsequently computed to represent this energy distribution along the Mel-scale frequency spectrum [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Mathematically it is expressed as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\left(Mel\\:Cepstral\\:Coefficient\\right)\\:c}_{i}=\\sqrt{\\frac{2}{L}}{\\sum\\:}_{m=1}^{L}\\:\\:lo{g}_{e}S\\left(m\\right)cos\\left[\\pi\\:i\\right(m-0.5\\left)\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:L\\)\u003c/span\u003e\u003c/span\u003e is the signal length and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m\\)\u003c/span\u003e\u003c/span\u003e is the Mel-scale frequency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.5.4 Smoothed Pseudo Wigner-Ville Distribution\u003c/h2\u003e \u003cp\u003eWVD serves as a method to examine the time-frequency properties of signals, providing a comprehensive view of signal behaviour in both time and frequency domains simultaneously. These spectrograms thus facilitate a deeper understanding of a signal's dynamic spectral characteristics, making them valuable tools in signal analysis [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. It is mathematically expressed as\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{W}_{x(t,\\nu\\:)}={\\int\\:}_{-\\infty\\:}^{+\\infty\\:}\\:\\:{x}^{\\:}(t+\\frac{\\tau\\:}{2}){x}^{*}(t-\\frac{\\tau\\:}{2}){e}^{-j2\\pi\\:\\nu\\:\\tau\\:}d\\tau\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe primary issue encountered with the WVD is cross-term interference. To mitigate this interference, the SPWVD is commonly employed. It is a potent method for analyzing signal energy in both time and frequency domains, offering insights into higher harmonics and precise time-domain localization. This technique employs time and frequency windows to minimize interference from cross-terms [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The SPWVD is mathematically expressed as follows:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{SW}_{g,h,X}(t,f)={\\int\\:}_{-\\infty\\:}^{\\infty\\:}\\:\\:{\\int\\:}_{-\\infty\\:}^{\\infty\\:}\\:x(t+\\frac{\\tau\\:}{2}){x}^{*}(t-\\frac{\\tau\\:}{2})g\\left(\\nu\\:\\right)h\\left(\\tau\\:\\right){m\\:e}^{-j2\\pi\\:f\\tau\\:}d\\nu\\:d\\tau\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere the function h(t) acts as a window to minimize cross-terms in the time domain, while \u003cem\u003eg(t)\u003c/em\u003e serves as a window to reduce cross-terms in the frequency domain.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Feature Extraction\u003c/h2\u003e \u003cp\u003eWe extracted GLCM, GLRLM, HM, ZM, FDTA, and FOS features from these spectrogram images. The GLCM utilizes second-order statistics to examine the texture by evaluating the relationships between pixels. This method typically involves analyzing pixel pairs to determine the frequency of specific combinations of brightness levels. Consequently, GLCM generates a matrix, with rows and columns corresponding to the gray values in the image, where each element denotes the frequency of specified pixel pairs [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] [\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. GLRLM stems from the observation that coarse textures tend to have longer gray-level runs, while fine textures consist mainly of shorter runs. It is denoted as \u003cem\u003ep(i, j)\u003c/em\u003e, the matrix defines the number of runs with pixels of gray level i and run length j. From this matrix, different texture features can be extracted [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. ZM serve as orthogonal descriptors that capture both global and geometric attributes of an image. The ZM of an image can be obtained by integrating the product of the image function and its corresponding Zernike polynomial over the unit circle. These polynomials are represented by equations defining radial and angular components. The amplitude of ZM remains invariant to rotation, making them useful for rotation-invariant feature extraction [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. FDTA serves to discern various features within an image, such as its textural properties, surface roughness, smoothness, overall area, and solidity [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. HM are computed to refine the matching process, unaffected by reflection, position, size, and orientation changes [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of Features Analysed in the Study\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTexture/Shape analysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFeatures\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGLCM (38)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContrast, Dissimilarity, Homogeneity, Energy (EN), Correlation, Angular Second Moment (ASM), Entropy, Mean, Variance, and Sum of Squares.\u003c/p\u003e \u003cp\u003eThe mean values and the range of values of the following features: 1) ASM, 2) Contrast, 3) Correlation, 4) Sum of Squares Variance (SSV), 5) Inverse Difference Moment (IDM), 6) Sum Average, 7) Sum Variance, 8) Sum Entropy (SE), 9) Entropy, 10) Difference Variance (DV), 11) Difference Entropy (DE), 12) Maximal Correlation Coefficient (MCC), 13) Information Measures of Correlation (IMC)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGLRLM (5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShort Run Emphasis (SRE), Long Run Emphasis (LRE), Grey Level Uniformity (GLU), Run Length Uniformity (RLU), and Run Percentage (RPC)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZM (24)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMoments 1 to 24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHM (7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMoments 1 to 7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFDTA (4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHurst Coefficients (HC) 1 to 4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFOS (7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean, Variance, Skewness, Kurtosis, Energy, Entropy, and Coefficient of Variation (CV)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e2.7 Feature Selection\u003c/h2\u003e \u003cp\u003eFeature selection is a vital component of classification tasks, aiding in speeding up learning processes by elimination of irrelevant features and enhancing accuracy. In this study, we utilized the RFECV method which selects features in a wrapper-style that iteratively identifies the most important subset of features by eliminating redundancy until attain the optimum number of features. Determining the ideal number of features is a critical hyper-parameter that needs careful tuning during training. This process is challenging because finding the right number of features to keep from the start can be complex. RFECV tackles this problem by using cross-validation to dynamically identify the optimal number of features. This approach improves classification performance by averaging the results across different validation folds [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e2.8 Classification\u003c/h2\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e2.8.1 Logistic Regression\u003c/h2\u003e \u003cp\u003eLR is a supervised learning algorithm used to estimate the probability of a categorical outcome based on multiple input features. It applies a logistic function to model the likelihood of a binary result.\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:f\\left(z\\right)=\\frac{1}{1+{e}^{-z}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:z={b}_{0}+{b}_{1}{x}_{1}+{b}_{2}{x}_{2}+\\cdots\\:+{b}_{n}{x}_{n}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{1}\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{n}\\)\u003c/span\u003e\u003c/span\u003e denotes n attributes, while b to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{n}\\)\u003c/span\u003e\u003c/span\u003e represent weights [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e] [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e2.8.2 Support Vector Machine\u003c/h2\u003e \u003cp\u003eSVM are used to separate data into different classes by using a hyperplane. When the data is not linearly separable in the original input space, SVM can apply nonlinear transformations to map the data into a higher-dimensional space. In SVM, each sample is represented as an m-dimensional vector and classified into two categories using an (m-1)-dimensional hyperplane. Out of all possible hyperplanes, the one that maximizes the margin which is the distance between the hyperplane and the closest data points from each class is chosen. This optimal hyperplane is essential for the performance of the SVM. The equation of the hyperplane in m-dimensional space is given by:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:y={W}_{0}+{W}_{1}{X}_{1}+{W}_{2}{X}_{2}+{W}_{3}{X}_{3}+\\dots\\:{W}_{m}{X}_{m}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:y={W}_{0}+\\sum\\:_{i=1}^{m}\\:{W}_{i}{X}_{i}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:={W}_{0}+{W}^{T}X$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:=b+{W}^{T}X$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, w is the weight vector consisting of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{3}\\)\u003c/span\u003e\u003c/span\u003e... \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{W}_{m}\\)\u003c/span\u003e\u003c/span\u003e, b is the bias term and X is a vector of input variables, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{2}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{3}\\)\u003c/span\u003e\u003c/span\u003e... \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{m}\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e2.8.3 Random Forest\u003c/h2\u003e \u003cp\u003eRF is a technique in ensemble learning that integrates multiple decision trees for both classification and regression tasks. It enhances the conventional bagging approach by introducing a layer of randomness. Unlike standard decision trees, in RF each node is divided based on a randomly chosen subset of predictors specific to that node, thereby mitigating overfitting while maintaining high predictive performance. Attribute selection in RF is guided by the Gini Index, which evaluates the impurity of a node and aids in determining the optimal split.\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:\\sum\\:_{\\:}\\:\\sum\\:_{j\\ne\\:i}\\:\\frac{f({C}_{i},T)}{\\left|T\\right|}*\\frac{f({C}_{j},T)}{\\left|T\\right|}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{i}\\)\u003c/span\u003e\u003c/span\u003e represents the class to which a randomly selected case, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e\u003c/span\u003e denotes the training data, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{f({C}_{i},T)}{\\left|T\\right|}\\)\u003c/span\u003e\u003c/span\u003e signifies the likelihood that the selected sample is assigned to the class \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{i}\\)\u003c/span\u003e\u003c/span\u003e [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e2.8.4 Extreme Gradient Boosting\u003c/h2\u003e \u003cp\u003eXGBoost is highly regarded for its scalability and outstanding performance while maintaining lower computational complexity. This gradient boosting classifier leverages decision trees to build a powerful prediction model by integrating several weak models into a single strong learner. The XGBoost algorithm trains multiple models in sequence, where each subsequent model aims to minimize the loss function of the overall system through gradient descent. This approach refines the model iteratively, enhancing the accuracy of predictions. The key idea behind XGBoost is to construct base learners that align with the negative gradient of the loss function [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e] [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e2.8.5 Performance Evaluation\u003c/h2\u003e \u003cp\u003eWe assessed the performance of classifiers using several metrics: accuracy, precision, sensitivity, F1-score, and the area under the receiver operating characteristic curve (ROC). Accuracy reflects the overall correctness of a model by counting the proportion of correct predictions across all categories. Sensitivity, also known as recall, measures effectiveness of the model in identifying the true positive instances, whereas specificity gauges its ability to correctly detect true negative cases. The F1-score combines precision and sensitivity into a single metric, offering a balanced view of the model's performance with respect to false positives and false negatives. The area under the curve (AUC) evaluates the model's ability to distinguish between classes by measuring the area under the ROC curve [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of performance metrics and their formula\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerformance metrices\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFormulae\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{TP+FP}{TP+FP+TN+FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSensitivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{TP}{TP+FN}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecificity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{TN}{TN+FP}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF1-score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{2*\\left(Recall*Precision\\right)}{Recall+Precision}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAUC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\int\\:}_{0}^{1}\\:\\:g\\left(x\\right)dx\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTP-True positive, FP- False positive, TN- True negative, FN- False negative, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:g\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the receiver operating characteristic curve.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eFigures 2 (a) and (b) show the average fMRI time series data for brain regions in individuals with ASD compared to TD subjects. The voxel intensity tends to be higher in the ASD group than in the TD group, though this difference does not occur consistently across all subjects and brain regions. Moreover, individuals with ASD display more irregular or less synchronized fluctuations in neural activity. These oscillations are well reflected in the respective time-frequency representation patterns shown in Figures (c-j). It can be observed that the signal consists of the lower frequency components which is clearly visible in the STFT as high intensity values in Figures (c) and (d). It reveals that the signal consists of more low frequency component compared to high frequency components. Furthermore, there are noticeable high fluctuations around 150 seconds in the ASD signal, which are depicted in the corresponding STFT spectrograms. In contrast, the TD group shows a more uniform intensity distribution in the STFT spectrograms. Similar patterns are observed in the spectrograms of CWT in Figures (e) and (f), MFC in Figures (g) and (h), and SPWVD in Figures (i) and (j).\u003c/p\u003e\n\u003cdiv\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure 2. Representation of average time series BOLD fMRI signal of a brain region of (a) ASD, (b) TD, corresponding spectrograms using (c), (d) STFT, (e), (f) CWT, (g), (h) MFC and (i), (j) SPWVD.\u003c/p\u003e\n\u003cp\u003eFigure 3 presents the classification results for the ROI that demonstrated the highest performance among the 236 ROIs analysed. The results were obtained using all 85 texture, shape, moment, FDTA, and FOS features extracted from the spectrograms with the LR, SVM, RF, and XGBoost classifiers. Figure\u0026nbsp;3 (a) illustrates the classification performance of the LR for all time-frequency methods, with CWT spectrograms achieving the highest accuracy of 73.57% for the network none in -34.7 35.6\u0026ndash;9.6 coordinates. Figure\u0026nbsp;3 (b) displays the SVM performance across different time-frequency methods, where STFT achieved the highest accuracy of 76.09% for the network cingulo-opercular task control (COTC) in 6.7 5 55.9 coordinates. Figure\u0026nbsp;3 (c) represents the RF classifier\u0026apos;s performance, with the MFC spectrograms attaining the highest accuracy of 78.92% for the network dorsal attention (DA) in 48.1 38.4 2.4 coordinates. Figure\u0026nbsp;3 (d) shows the classification performance of XGBoost, where the MFC spectrograms achieved the highest accuracy of 80.38% for the network somatosensory motor hand (SMH) in -5 -28.2 60.4 coordinates. It can be noted that the top performing spectrograms and corresponding networks are inconsistent between the classifiers. Notably, the XGBoost model consistently outperformed the LR, RF, and SVM classifiers across various spectrograms. The highest performance metrics for the XGBoost with MFC spectrograms achieved an accuracy of 80.38%, sensitivity of 77.77%, specificity of 82.85%, F1-score of 80.27%, and AUC of 80.31%, utilizing all 85 features.\u003c/p\u003e\n\u003cdiv\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure 3. Classification performance comparison across time-frequency methods and classifiers considering all 85 features and their corresponding networks (a) LR, (b) SVM, (c) RF and (d) XGBoost\u003c/p\u003e\n\u003cp\u003eFurthermore, we applied RFECV in our analysis to identify the optimal features for input to classifiers, aiming to enhance model performance. Figure\u0026nbsp;4 presents the classification results for the ROI that demonstrated the highest performance among the 236 ROIs analysed using only the optimal features selected from the 85 texture, shape, moment, FDTA, and FOS features. Figure\u0026nbsp;4 (a) illustrates the classification performance of the LR across all time-frequency methods, with SPWVD spectrograms achieving the highest accuracy of 86% using 5 distinct features optimized by RFECV for the network DA in 36.8 37.8 13.1 coordinates. Figure\u0026nbsp;4 (b) displays the SVM performance across different time-frequency methods, where MFC achieved the highest accuracy of 95.71% with the top 36 optimal features for the network fronto-parietal task control network (FPTC) in -5.5 29.3 44 coordinates. Figure\u0026nbsp;4 (c) represents the RF classifier\u0026apos;s performance, with MFC spectrograms attaining the highest accuracy of 87.33% by using 25 optimal features for the network FPTC in 38.9 9.6 42.7 coordinates. Figure\u0026nbsp;4 (d) shows the classification performance of XGBoost, where MFC spectrograms achieved the highest accuracy of 85.9% with 26 optimal features for the network SMH in -5 -28.2 60.4 coordinates. It is notable that the top-performing spectrogram (MFC) is consistent between the SVM, RF, and XGBoost classifiers. However, number of features required for the top performing model and corresponding networks varied across the classifiers. The SVM model consistently outperformed the LR, RF, and XGBoost classifiers across various spectrograms. The highest performance metrics for the SVM with MFC spectrograms were an accuracy of 95.71%, sensitivity of 100%, specificity of 91.42%, F1-score of 95.76%, and AUC of 95.71%, utilizing 36 optimal features out of the 85 total features identified by RFECV. The findings demonstrate a significant improvement in performance when incorporating RFECV into our model.\u003c/p\u003e\n\u003cdiv\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure 4. Classification performance comparison across time-frequency methods and classifiers using optimum features using RFECV and their corresponding networks (a) LR, (b) SVM, (c) RF and (d) XGBoost\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan\u003e5\u003c/span\u003e represents the ranking of the 36 optimal features identified by RFECV that contributed to the top-performing MFC-SVM model. Among these 36 features, GLCM, ZM, HM, GLRLM, FDTA and FOS contributed 15, 10, 5, 3, 2, and 1 feature respectively. It is evident that each feature group plays a role in the analysis. The most important feature is from the GLCM (homogeneity), followed by features from the FDTA (HC-3) and the ZM (radius-9-12) group. Notably, 36 out of the 85 features strike a balance, as the model\u0026apos;s performance deteriorates when the number of features considered is either too low or too high.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan\u003e6\u003c/span\u003e illustrates the region-wise performance of the MFC-SVM model using optimized features. Notably, the classification performance differed significantly across various brain regions and their associated networks. Certain regions exhibited superior classification performance, highlighting their greater relevance for analysis compared to considering all ROIs. This approach reduces computational costs and allows clinicians to focus on specific brain areas that have a greater impact on ASD. The highest performance accuracy was achieved for the FPTC (-5.5 29.3 44 coordinates) network at 95.71%, followed by 93.21% for none (-34.7 35.6\u0026ndash;9.6 coordinates) and 88.76 for the COTC (36.7 5.2 12.7 coordinates) while the lowest was for the COTC (8.6 4.2 40.1 coordinates) network at 40.95%. This comprehensive analysis provides insights into the effectiveness and reliability of various time-frequency methods and classifiers across different brain regions, aiding informed decision-making in ASD diagnosis using neuroimaging.\u003c/p\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study explores the development of classification models such as LR, SVM, RF, and XGBoost for ASD, utilizing a combination of spectrogram time-frequency techniques such as STFT, MFC, CWT, and SPWVD, along with features like GLCM, FDTA, FOS, HM, GLRLM, and ZM extracted from 236 ROIs. We achieved accuracy of 80.38% and 95.71% using all features and optimum features by RFECV with 5-fold cross-validation approach. We found that FPTC network from \u0026minus;\u0026thinsp;5.5 29.3 44 coordinates produced the highest classification accuracy. Additionally, the top performing features are homogeneity, Hurst coefficient-3 and radius-9-12 from GLCM, FDTA and ZM group respectively. These findings could lead to future research on developing more sophisticated ASD classification systems. Such research might take a regional approach, focusing on various brain areas rather than individual subjects.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of previous studies using time-frequency methods on fMRI BOLD signals for ASD diagnosis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStudy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDatabase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSites (subjects)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAtlas\u003c/p\u003e \u003cp\u003e(Regions)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTime frequency\u003c/p\u003e \u003cp\u003emethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFeature extraction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCross-validation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eClassifier\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eFeature selection\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003ePerformance (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNetwork\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOur study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE-I and ABIDE-II\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOHSU\u003c/p\u003e \u003cp\u003e(36 ASD, 35 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGordon's, HO, Diedrichsen (236)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSTFT, CWT, MFC, SPWVD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGLCM, GLRLM, ZM, HM, FDTA and FOS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5-fold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eLR, SVM, RF, XGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eRFECV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy-95.71, sensitivity-100, specificity-91.42, F1-score-95.76, AUC-95.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eSMH, COTC, FPTC, DA, CPTC, SC, Visual, Auditory, Default\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE-I and ABIDE-II\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOHSU\u003c/p\u003e \u003cp\u003e(36 ASD, 35 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGordon's, HO, Diedrichsen (236)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGLCM, GLRLM, ZM, HM, FDTA and FOS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5-fold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCatBoost, DT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy \u0026minus;\u0026thinsp;83.04, Sensitivity \u0026minus;\u0026thinsp;66.66, Specificity- 85.57, F1 score \u0026minus;\u0026thinsp;75.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eRST\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003cp\u003e(41 ASD, 41 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAAL\u003c/p\u003e \u003cp\u003e(116)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePFT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGooglenet, DenseNet201, Resnet18, and Resnet101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5-fold, 10-fold, 15-fold and 20-fold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSVM,\u003c/p\u003e \u003cp\u003eKNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy- 96.7, Sensitivity- 96.6, Specificity- 96.9, Precision- 96.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSDSU,\u003c/p\u003e \u003cp\u003eSTANFORD,\u003c/p\u003e \u003cp\u003eUM,\u003c/p\u003e \u003cp\u003eKKI,\u003c/p\u003e \u003cp\u003eLEUVEN,\u003c/p\u003e \u003cp\u003eSBL,\u003c/p\u003e \u003cp\u003eTRINITY,\u003c/p\u003e \u003cp\u003eCALTECH,\u003c/p\u003e \u003cp\u003eCMU,\u003c/p\u003e \u003cp\u003eMAX, NYU,\u003c/p\u003e \u003cp\u003eOHSU,\u003c/p\u003e \u003cp\u003eOLIN; PITT,\u003c/p\u003e \u003cp\u003eUCLA,\u003c/p\u003e \u003cp\u003eUSM, YALE,\u003c/p\u003e \u003cp\u003e(505 ASD,\u003c/p\u003e \u003cp\u003e530 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAAL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eWC, PWC FC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10-fold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy- 95.2, Sensitivity- 96.7, Specificity- 94.3, Precision- 94.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCALTEC, CMU, KKI\u003c/p\u003e \u003cp\u003e(41 ASD, 41 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAAL\u003c/p\u003e \u003cp\u003e(116)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGooglenet, DenseNet201, Resnet18, and Resnet101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNo cross-validation\u003c/p\u003e \u003cp\u003e(Training-70%, Validation-15% and testing-15%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSVM, KNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy- 85.9, Sensitivity- 79.3, Specificity- 92.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNYU, SBL, SDSU, TRINITY, YALE, USM, KKI, UM\u003c/p\u003e \u003cp\u003e(36 ASD, 36 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAAL\u003c/p\u003e \u003cp\u003e(116)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eWC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5-fold, 10-fold, 15-fold, 20-fold, leave-one site validation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy-89.8, Sensitivity- 90.1, Specificity \u0026minus;\u0026thinsp;89.7, Precision- 89.6, F1 score-9.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNDAR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003cp\u003e(50 ASD, 50 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4-fold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy-86, Sensitivity- 82, Specificity\u003c/p\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eCG, STG, PAC, AG\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eABIDE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYALE, PITT, UCLA, SDSU, NYU, TRINITY\u003c/p\u003e \u003cp\u003e(222 ASD, 246 TD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHO\u003c/p\u003e \u003cp\u003e(111)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD3TDWT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGARCH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5-fold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003et-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAccuracy- 75.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eMTG, SG, PGR\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ePFT-Progressive Fourier Transform, CALTECH-California Institute of Technology, CMU- Carnegie Mellon University, NYU-New York University, SBL-Social Brain lab, SDSU- San Diego State University, Trinity-Trinity College Institute of Neuroscience, YALE-Yale School of Medicine, USM-University of Utah School of Medicine, KKI-Kennedy Krieger Institute, UM-University of Michigan, D3TDWT-Double-Density Dual-Tree Discrete Wavelet Transform, GARCH-Generalized autoregressive conditional heteroscedasticity, AAL-Automated anatomical labeling, PITT- University of Pittsburgh School of Medicine, UCLA- University of California Los Angeles, STANFORD- Stanford University; UM-University of Michigan, LEUVEN-University of Leuven, MAX-Ludwig Maximilian University of Munich, OLIN-Olin Center; Institute of Living at Hartford Hospital, WC-Wavelet coherence, PWC-Principal wavelet coherence, MTG-Middle Temporal Gruys, SG-Supramarginal Gyrus, PGR-Paracingulate Gyrus R, CG-Cingulate gyri, STG-Superior temporal gyrus, PAC-Primary auditory cortex and AG-Angular gyrus, FPTC-Fronto-parietal task control network, CPTC- Cingulo Parietal Task Control\u003c/p\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Effect of time-frequency methods\u003c/h2\u003e \u003cp\u003eIn this study, BOLD time-series signals were analysed using four distinct time-frequency methods: STFT, CWT, MFC, and SPWVD, to generate spectrograms. These spectrograms served as the basis for feature extraction, which were then input into machine learning classifiers to evaluate model performance. Initially, the model demonstrated superior performance with MFC spectrograms, followed by STFT, SPWVD, and CWT, when utilizing all 85 features. However, upon employing RFECV for optimal feature selection, the model consistently outperformed with the MFC method, followed by CWT, STFT, and SPWVD. The adaptive nature of the MFC method, with its ability to provide a sparse representation focusing on low-frequency components, is useful for effectively capturing and highlighting the most relevant features of the BOLD signal, leading to improved performance of machine learning models in tasks such as ASD classification. This may also be attributed to the MFC spectrogram's generation process, which converts a signal's linear frequency scale to a logarithmic Mel scale using the STFT. This spectrum is then processed through a filter bank to determine the energy distribution across the Mel-scale frequency range. Eigenvalues are computed to represent this distribution, leading to improved performance of machine learning models. Our study demonstrates the superiority of MFC over traditional time-frequency methods like STFT, CWT, and SPWVD in analysing fMRI data [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Notably, previous studies have explored various methods, including CWT [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], PFT [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], WC [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e], D3TDWT [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], and a combination of WC, PWC, and FC [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. However, these studies did not conduct comparative analyses of distinct time-frequency methods, nor did they delve into the effects of STFT, MFC, and SPWVD in analysing BOLD time signals from fMRI. This comprehensive examination sheds light on the nuanced performance differences between these time-frequency methods and underscores the superiority of MFC spectrograms in ASD classification.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Impact of features\u003c/h2\u003e \u003cp\u003eIn this study, we analysed a total of 85 features including texture and shape-based patterns. However, the optimal feature set for achieving the best accuracy with the MFC method and SVM classifier comprised 36 out of these 85 features. These features were categorized into groups such as GLCM, GLRLM, HM, ZM, FDTA, and FOS. Among these, the top-performing features were homogeneity from the GLCM group, the Hurst coefficient-3 from the FDTA group, and radius-9-12 from the ZM group. The specific features performed well due to their ability to capture essential characteristics of the BOLD signals. Homogeneity from the GLCM group reflects the similarity of pixel intensities, which is crucial for identifying consistent patterns in fMRI data [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The Hurst coefficient-3 from the FDTA group is indicative of the fractal nature of the time-series data, effectively capturing long-term patterns and self-similar structures [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The radius-9-12 feature from the ZM group provides a robust representation of image shapes and patterns, contributing to more accurate signal characterization [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. In conclusion, the study highlights that a carefully selected subset of features significantly enhances the performance of machine learning models, with MFC-derived features demonstrating superior effectiveness in ASD classification. The number of selected features used for classification with respective time-frequency methods and classifiers, identified through the RFECV method for each region that performed better for different classifiers and corresponding time-frequency methods. Supplementary table 1 highlights the consistency of features among different time-frequency methods and classifiers. Notably, the highest contributing feature, ZM radius_9_2, consistently appeared 8 times in the analysis. Additionally, GLCM_MCC _Range, ZM radius_9_6, ZM radius_9_11, and FDTA HC_4 each contributed 7 times, among the total 85 features. However, studies never used these features in ASD classification using fMRI BOLD signals.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Impact of feature selection\u003c/h2\u003e \u003cp\u003eOur study examined effect of feature selection methods and classifiers in ASD classification. We employed two different approaches utilizing all available features and utilizing only the optimal subset of features identified through RFECV. When utilizing all 85 features for classification, the results demonstrated an accuracy of 80.38%, sensitivity of 77.77%, specificity of 82.85%, F1-score of 80.27%, and AUC of 80.31%. In contrast, the SVM classifier achieved the best performance when using the MFC spectrogram in combination with RFECV. It yielded an overall accuracy of 95.71%, sensitivity of 100%, specificity of 91.42%, F1-score of 95.76%, and AUC of 95.71%. This result was obtained using the top 36 important features. Before applying RFECV, the classification model's performance with all 85 features showed moderate accuracy and balanced sensitivity and specificity. However, including all features likely introduced noise and irrelevant data, reducing the model\u0026rsquo;s ability to detect key patterns crucial for ASD classification. After applying RFECV, performance improved significantly. By selecting the most relevant 36 features, RFECV filtered out redundant and irrelevant data, allowing the model to focus on the most informative aspects of the BOLD signals. This refined feature set led to significant improvements in accuracy, sensitivity, specificity, F1-score, and AUC. These results highlight the effectiveness of RFECV in enhancing model performance. Further, RFECV improves performance by systematically evaluating the contribution of each feature and recursively removing the least significant ones. This process helps in reducing overfitting by eliminating noise and redundant features, enhancing computational efficiency with fewer features leading to faster training and prediction times, and improving model interpretability as a smaller set of relevant features makes the model easier to interpret and understand [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Studies have shown that optimal feature selection enhances the accuracy and robustness of machine learning models across various applications, including medical diagnostics, image processing, and signal analysis [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. This study's findings show that using RFECV for optimal feature selection can significantly improve the accuracy and efficiency of ASD classification models. This approach not only improves the overall performance metrics but also contributes to a more streamlined and interpretable model, facilitating better clinical and research applications.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Effect of Classifiers\u003c/h2\u003e \u003cp\u003eAcross various time-frequency methods, we observed notable variations in classification performance. MFC stood out as particularly effective, achieving an impressive accuracy of 80.38% using XGBoost classifier. Similarly, the STFT method performed commendably with an accuracy of 78.85% using XGBoost classifier. Conversely, the CWT showed noteworthy accuracy of 75.89% using SVM, and the SPWVD method demonstrated respectable accuracy, reaching 76.25% using XGBoost classifier. However, the application of RFECV for feature selection resulted in significant improvements in classification accuracy across diverse time-frequency methods, classifiers, and associated brain networks. Notably, the highest accuracies were achieved with STFT yielding 88.76% accuracy using SVM classifier, CWT achieving 93.21% using SVM, MFC obtaining 95.71% using SVM, and SPWVD reaching 86% using LR classifier. Among the classifiers tested, the SVM consistently outperformed others in processing BOLD signals. The superior performance of SVM can be attributed to its capability to effectively manage complex data and determine the optimal boundary for distinguishing between different groups [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. This is particularly beneficial in analysing complex fMRI data where the distinction between ASD and TD patterns may be subtle and multidimensional. While previous studies have achieved high classification accuracy through the use of intricate deep learning algorithms for feature extraction, their analyses often lack network-based approaches. For instance, [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] achieved commendable results but did not incorporate network-based methods. Similarly, although a few studies have conducted region-wise analyses, such as those by [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], our model's performance surpasses these prior studies. Specifically, [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] utilized statistical t-tests for feature selection, yet our model's performance exceeds. This superior performance can be partly attributed to our use of a homogeneous and balanced dataset, derived from a single site, which minimizes variability and enhances the reliability of our findings. In conclusion, this study's findings demonstrate that integrating RFECV for optimal feature selection and utilizing SVM classifiers notably improves the accuracy of ASD classification models. This approach not only improves overall performance metrics but also offers a more refined and interpretable model, which is crucial for advancing diagnostic accuracy and treatment strategies in ASD research.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Region-based analysis and clinical implications\u003c/h2\u003e \u003cp\u003eOur analysis of 236 brain regions provides a foundation for future investigations into key contributors to ASD diagnosis. Previous studies using region-based approaches have often yielded inconsistent findings [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. In our study, we identified several influential networks and their respective pipelines: COTC (STFT-LR, STFT-SVM, STFT-RF, CWT-RF), SMH (MFC-XGBoost), FPTC (CWT-XGBoost, MFC-SVM), DA (SPWVD-LR), CPTC (SPWVD-RF), None (STFT-XGB, CWT-LR, SPWVD-SVM), Visual (CWT-SVM), Auditory (SPWVD-XGBoost), and Default (STFT-RF), utilizing all 85 features. Following RFECV, the networks that remained influential were COTC (STFT-SVM, CWT-RF), SMH (MFC-XGBoost), FPTC (MFC-SVM), DA (SPWVD-LR), CPTC (SPWVD-RF), SC (SPWVD-SVM), Visual (STFT-LR), Auditory (SPWVD-XGBoost), None (CWT-LR, CWT-SVM, CWT-XGB, MFC-LR) and Default (STFT-RF). Previous research has highlighted the involvement of various networks such as COTC, Default [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], RST, VA, FPTC, and Visual [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], CG, STG, PAC, AG [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], MTG, SG, PGR [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The networks identified in our study primarily involve cortical regions (COTC, Default, FPTC, SMH, DA, CPTC, Visual, Auditory) and SCregion. Research has identified associations in ASD with smaller SC volumes in the pallidum, putamen, amygdala, and nucleus accumbens, along with increased cortical thickness in the frontal cortex and reduced thickness in the temporal cortex. Age-related analyses reveal altered cortical thickness development in ASD, with notable differences emerging around adolescence. Notably, no age-by-ASD interactions were found in SC regions. These findings deepen our understanding of ASD\u0026rsquo;s neurobiological basis, highlighting both structural differences and developmental patterns in affected individuals [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e4.6. Effect of process pipeline\u003c/h2\u003e \u003cp\u003eIn this study, we evaluated the impact of different process pipelines on ASD classification performance by analyzing four time-frequency methods (STFT, CWT, MFC, and SPWVD), four classifiers (LR, XGBoost, RF, and SVM), 236 brain regions, and two feature selection approaches: using all 85 features and using the optimal feature subset identified through RFECV. Among the tested pipelines, the highest performance was achieved by the MFC-XGBoost pipeline using all 85 features for the SMH region [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] and the MFC-SVM pipeline using the optimal features selected by RFECV for the FPTC region [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. The MFC-XGBoost pipeline performed well due to XGBoost robust gradient boosting framework, which excels in handling structured data and preventing overfitting through regularization techniques. The combination of MFC's ability to capture sparse and low-frequency features of the BOLD signals with XGBoost powerful classification capability enabled this pipeline to effectively distinguish between ASD and TD subjects [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Similarly, the MFC-SVM pipeline achieved high performance when using the optimal features selected by RFECV. SVM is known for its effectiveness in high-dimensional spaces, which makes it well-suited for analysing fMRI data [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. The use of MFC provided a detailed representation of the signal characteristics, while RFECV ensured that only the most relevant features were used, thereby improving the model's performance [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Previous studies have shown that incorporating advanced algorithms like XGBoost and SVM, along with effective feature selection techniques, can significantly improve the accuracy of medical diagnostic models [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In conclusion, the findings of this study underscore the importance of a well-designed process pipeline in improving ASD classification accuracy. These pipelines leveraged the strengths of their respective classifiers and the detailed feature representation provided by MFC, resulting in superior classification performance. This study highlights the potential of combining advanced feature extraction, selection methods, robust classifiers and specific network to enhance diagnostic accuracy and contribute to more effective ASD research and clinical applications.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e4.7. Limitations and future scope\u003c/h2\u003e \u003cp\u003eOur study highlights the significant potential of MFC spectrograms followed by CWT, STFT and SPWVD spectrograms for identifying biomarkers for diagnosing ASD. However, several limitations must be addressed before this method can be applied in clinical settings. First, the method needs to be validated on a larger dataset and with a comprehensive classification model to confirm its robustness and generalizability. Our research exclusively employed machine learning classifiers without incorporating deep learning techniques. Deep learning models, although more data and resource-intensive, could potentially enhance clinical diagnosis accuracy. The current approach is limited by a small sample size, including only 36 individuals with ASD and 35 TD individuals. This limited sample necessitates validation on larger and more diverse datasets. Moreover, our study did not classify all sites as previous works have done, which could affect the generalization of our findings. Future research should explore lightweight deep learning models to enhance diagnostic accuracy while addressing the computational constraints common in healthcare settings. These models could offer more refined insights despite data and computational challenges. Crucial next steps include conducting longitudinal studies and applying our methodology to diverse datasets. This approach will enable us to track the progression of ASD over time and validate our findings across diverse demographic groups and clinical profiles. By examining neurodevelopmental trajectories in ASD and extending these methods to other neurodevelopmental disorders, we can achieve a more comprehensive understanding of these conditions. Additionally, efforts should prioritize enhancing the accessibility and practicality of advanced neuroimaging techniques in clinical practice. Incorporating these methods into routine diagnostic procedures requires addressing logistical challenges to ensure their widespread adoption and usefulness. This integration will be essential for enhancing diagnostic precision and optimizing treatment planning for ASD.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThrough this study, we explored the potential of using different time-frequency methods to analyse BOLD time-series signals from fMRI Data for ASD Classification. We employed four distinct methods: STFT, CWT, MFC, and SPWVD to generate spectrograms. These spectrograms were then used to extract various features, including GLCM, GLRLM, FDTA, HM, ZM, and FOS, which were input into machine learning classifiers LR, SVM, RF and XGBoost to evaluate their performance. Our findings revealed that MFC spectrograms consistently exhibited the highest performance, achieving an accuracy of 80.38% when all 85 features were used with XGBoost and 95.71% when optimal features were selected using RFECV and SVM. Comparative analyses with previous studies indicate that while various methods have been employed to classify ASD, our approach stands out due to its comprehensive comparative analysis of distinct time-frequency methods and the integration of optimal feature selection strategies. Prior research often lacked network-based analyses and did not explore the combined effects of STFT, MFC, and SPWVD in detail. Our study bridges this gap, offering valuable insights into the effectiveness of various time-frequency methods and highlighting the crucial role of feature selection. Moreover, our analysis included an extensive region-based approach, identifying specific brain networks such as the Visual, COTC, Default, None, FPTC, SMH, DA, SC, CPTC, Auditory as significantly contributing to the classification accuracy. These findings suggest that future research should focus on these networks for improved diagnostic precision. In conclusion, this study demonstrates the effectiveness of using spectrograms and optimal feature selection techniques in accurately classifying ASD. These promising results underscore the potential of these methods for early diagnosis and intervention in clinical settings. They pave the way for more refined and reliable diagnostic tools for ASD.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflict of interest:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval:\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data used in the study from the publicly available ABIDE database.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability statement:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data used for this study was obtained from the publicly available ABIDE database https://fcon_1000.projects.nitrc.org/indi/abide/.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding statement:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research has received support from the Indian Council of Medical Research (ICMR), reference number R\u0026amp;D/SA/ICMR/BME/24-25/02/588.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement:\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors also acknowledge the PARAM Shivay supercomputer facility at IIT BHU, Varanasi, India, for their valuable assistance during this study.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eL. 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Psychiatry\u003c/em\u003e, vol. 11, p. 551808, Sep. 2020, doi: 10.3389/fpsyt.2020.551808. \u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Supplementary Table 1","content":"\u003cp\u003eSupplementary Table 1 is not available with this version\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Autism spectrum disorder, fMRI, time-frequency spectrograms analysis, feature extraction, machine learning","lastPublishedDoi":"10.21203/rs.3.rs-5170177/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5170177/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, our goal was to develop a diagnostic framework for autism spectrum disorder (ASD) by analyzing time-frequency spectrograms generated from BOLD signals in functional magnetic resonance imaging (fMRI) data. We used fMRI data from the Autism Brain Imaging Data Exchange (ABIDE) database and performed brain parcellation with Gordon\u0026rsquo;s, Harvard-Oxford, and Diedrichsen atlases. Time-frequency spectrograms were generated from the average time series of each region of interest (ROI) using methods like short-time Fourier transform, continuous wavelet transform, Mel frequency cepstrum (MFC), and smoothed pseudo Wigner-Ville distribution. From these spectrograms, we extracted various features, including the grey-level co-occurrence matrix, grey-level run-length matrix, fractal dimension texture analysis, Zernike moments, Hu moments, and first-order statistics. To evaluate the diagnostic model, we applied machine learning classifiers, including logistic regression, support vector machine (SVM), extreme gradient boosting, and random forest, alongside recursive feature elimination with 5-fold cross-validation (RFECV) and hyperparameter tuning. The SVM classifier using MFC spectrograms and RFECV yielded the highest performance, achieving an overall accuracy of 95.71%, sensitivity of 100%, specificity of 91.42%, F1-score of 95.76%, and area under the curve (AUC) of 95.71% with the top 36 features for the fronto-parietal task control network. In contrast, utilizing all 85 features for the somatosensory motor hand network resulted in an accuracy of 80.38%, sensitivity of 77.77%, specificity of 82.85%, F1-score of 80.27%, and AUC of 80.31%. These findings underscore the model's potential in the precise classification of ASD, offering valuable implications for early diagnosis and intervention.\u003c/p\u003e","manuscriptTitle":"Advancing ASD diagnostic classification using time-frequency spectrograms of fMRI BOLD signals and machine learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-13 06:36:31","doi":"10.21203/rs.3.rs-5170177/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9ba63abe-9812-4ba4-8373-eb918aa66ec5","owner":[],"postedDate":"November 13th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-03-20T03:53:27+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-13 06:36:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5170177","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5170177","identity":"rs-5170177","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}