Machine-learning classification of postural sway in young adults during colored noisy vestibular stimulation

Machine-learning classification of postural sway in young adults during colored noisy vestibular stimulation | 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 Machine-learning classification of postural sway in young adults during colored noisy vestibular stimulation Negar Rahimi, Vassilia Hatzitaki, Alireza Kamankesh, Alkistis Gavriilidou, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6306483/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 We compared the accuracy with which a machine-learning algorithm could distinguish among center-of-pressure (CoP) trajectories during upright standing when noisy galvanic vestibular stimulation (nGVS) was applied at intensities relative to the perceptual threshold. This report comprises a secondary analysis of data published in Gavriilidou et al. (2025). The k-nearest neighbor (KNN) algorithm was used to classify CoP trajectories recorded while young healthy adults stood on a firm surface with feet together and eyes closed. From 7 variables in the time domain and 84 bandwidths in each axis in the time-frequency domain, the three most important features in the time domain and two in the time-frequency domain were selected by permutation feature importance and correlation-based feature selection techniques, respectively. Models were developed to determine classification accuracy in four conditions derived from combinations of stimulus intensity (% perceptual threshold), type of superimposed noise (Pink or White), and the responsiveness of participants to the perturbation. Classification accuracy was >96% in all four conditions, which indicates that the CoP trajectories were unique at each level within the four conditions. Critically, the machine-learning model was able to discriminate the features extracted from CoP trajectories for participants who either did or did not exhibit a stochastic-resonance effect in response to nGVS. Moreover, SHapley Additive exPlanation analysis found that the contribution of the five extracted features in classifying these two groups of participants was greater during the White-noise condition. These results indicate that nGVS had unique effects on CoP trajectories within each of the four conditions. K-Nearest Neighbor Algorithm Standing Posture Vestibular Stimulation Colored Noise Stochastic Resonance Continuous Wavelet Transform Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION The concept of stochastic resonance asserts that a signal too weak to be detected by a sensor can be boosted by the addition of noise (Di Ponzio et al. 2024 ; McDonnell and Abbott, 2009 ; McLaren et al. 2023 ; Nooristani et al. 2021 ). This method has been used in the field of balance control to modulate the function of the vestibular system and associated networks (Gavriilidou et al. 2025 ; Mitsutake et al. 2024 ). It has been shown, for example, that the application of noisy galvanic stimulation at imperceptible intensities can enhance vestibular perception and improve several features of the center-of-pressure trajectories during upright standing (Inukai et al. 2018 ; Matsugi et al. 2020 ). However, the effect varies across individuals, depending on such factors as stimulus characteristics, balance-control metric, age, and the functional status of the vestibular system (Asslälander et al. 2021; Inukai et al. 2018 ; Iwasaki et al. 2014 ; Nooristani et al. 2021 ). Critically, the benefit of stochastic resonance is greatest at intermediate levels of added noise (Galvan-Garza et al. 2018 ; Gavriilidou et al. 2025 ; Nooristani et al. 2021 ; Stone et al. 2025 ). The presence of a stochastic-resonance effect is typically determined by comparing the shape of a plot that shows the influence of added noise on an outcome variable across a range of stimulus intensities with a function (pseudo-bell-shaped curve) used to characterize the phenomenon (Galvan-Garza et al. 2018 ; Stone et al. 2025 ). The outcome variables can comprise measures of perceptual threshold (Galvan-Garza et al. 2018 ; Stone et al. 2025 ) or balance-control metrics (Asslälander et al. 2021; Gavriilidou et al. 2025 ; Nooristani et al. 2021 ). Expert analysis of the plots has revealed that the proportion of individuals exhibiting a stochastic-resonance effect varies from 10–78% across a broad range of study designs and outcome measures (Asslälander et al. 2021; Galvan-Garza et al. 2018 ). The current report comprises a secondary analysis of data that were published in Gavriilidou et al. ( 2025 ). The purpose of that study was to evaluate the influence of two types of noisy galvanic vestibular stimulation (nGVS) on postural sway (CoP displacement) when young adults stood upright on a firm surface with feet together and eyes closed. nGVS intensity was set relative to the perceptual threshold of a cutaneous sensation elicited by the stimulation. At a group level, they found that the mean velocity of the CoP trajectory increased with stimulus intensity for the Pink-noise condition, but not for the White-noise condition or for either of the other two postural-sway metrics. Underlying these weak group effects, the responses exhibited by individual participants, as assessed by expert raters, were variable with 55% of the participants during the White-noise condition and 30% during the Pink-noise condition displaying a stochastic-resonance effect. An alternative approach to determine the influence of nGVS on postural sway is to apply machine-learning models to detect meaningful features within each condition (Daneshgar et al. 2024 ; Dahiya et al. 2022 ; Fadil et al. 2021 ; Kamankesh et al. 2025 ; Osisanwo et al. 2017 ; Rahimi et al. 2025 ; Stone et al. 2025 ). The purpose of our study was to compare the accuracy of a machine-learning algorithm in distinguishing features extracted from CoP trajectories during upright standing when nGVS was applied at intensities relative to perceptual threshold. This approach used the information embedded in the time and time-frequency series of the CoP trajectories to assess their uniqueness within each of the four conditions. We hypothesized that distinct CoP trajectories could be identified due to the influence of stimulus intensity, type of superimposed noise, and the responsiveness of participants to the perturbation. METHODS This report is based on a secondary analysis of data that have already been published (Gavriilidou et al. 2025 ). The purpose of that study was to evaluate the influence of nGVS on postural control when young adults stood upright on a firm surface with feet together and eyes closed. The study was performed at Aristotle University in Thessaloniki, Greece, and the protocol was approved by the Institutional Research Ethics and Ethics Committee (approval number 145/15.3.2023). Experimental data In a single experimental session, 40 healthy adults (25.1 ± 5.6 years, 21 females) performed two tasks: (1) assessment of cutaneous perception threshold; and (2) measurement of CoP trajectories in the absence (baseline) and presence of nGVS added to seven stimulus intensities. Each participant was assigned to a group that received either White or Pink noise generated in LABVIEW (version 8.6, National Instruments) using the “Gaussian White Noise” or the “Inverse fNoises Waveform IV” functions, respectively. These signals were smoothed with a second-order Butterworth filter (≤ 30 Hz). The signals had a zero mean, with the standard deviation (for white noise) and noise density (for pink noise) scaled to each of the 7 stimulus intensities: 50, 60, 70, 80, 90, 100, and 110% of the perceptual threshold. Perceptual threshold was estimated as the lowest stimulus intensity at which the seated participants were able to detect a cutaneous sensation elicited by the applied stimulation. The stimulus was generated with a National Instruments device (NI PCI-6221) and delivered through a pair of rubber electrodes (PG980/2, Silicone Reusable Electrode 60x85 mm, Neurocare group AG, Germany) attached behind the ears with the cathode placed over the left mastoid. The stimulus was applied for 10 s at an increasing intensity in steps of 0.5 mA. The time between each stimulus intensity varied randomly within the range of 15 to 20 s. The average (mean ± standard deviation) current at which the perceptual threshold was detected was 410 ± 120 µA for the White-noise group and 432 ± 137 µA for the Pink-noise group. The standing balance task was performed on a force platform (model 6501, Bertec Corporation) that measured the three orthogonal components of the ground reaction force. Participants stood with feet together and eyes closed. Each trial lasted 60 s with nGVS being applied from 30 to 60 s during each of 7 trials. The order of the 7 levels of nGVS intensity was randomized across trials. Prior to performing the nGVS trials, participants completed one trial with no stimulation (baseline trial). Data analysis Postural sway during each trial was quantified with three metrics derived from the CoP trajectory in the forward-backward and side-to-side directions (Fig. 1 ). The ground reaction force was digitized at 1000 Hz, down-sampled to 100 Hz, and low-pass filtered with a second-order Butterworth filter (cutoff frequency: 6 Hz). As a result of this processing, each 60-s trial comprised 6,000 data points in each of the two directions. The three metrics comprised: (1) the root-mean-square value of the CoP displacement in the side-to-side direction; (2) the mean CoP velocity in the side-to-side direction; and (3) the area of an ellipse that enclosed 90% of the trajectory. These metrics were calculated for the period of no nGVS (5–30 s) and the interval during which nGVS was applied (30–55 s), which in each instance involved reducing the 2,500 data points to a single value. These metrics were then used to categorize individual CoP trajectories as exhibiting stochastic resonance or not. The influence of nGVS on the postural-sway metrics was examined by Gavriilidou et al. ( 2025 ) at both the group and individual levels. In the current report, we focus on the results obtained at the individual level. The analysis examined the influence of each type of nGVS (White or Pink noise) on the relative changes in the postural-sway metrics across the 7 stimulus intensities. Specifically, a reduction in the normalized value of a metric at intermediate stimulus intensities (characteristic Bell-shaped curve) was interpreted as evidence of a stochastic-resonance effect. Three experts examined the plots and independently rated the data for each condition (type of noise, stimulus intensity, and postural-sway metric) as being best fit with a linear function or the characteristic Bell-shaped curve (Galvan Garza et al. 2018; Stone et al. 2025 ). When two or three raters deemed that the data for at least 2 of the 3 postural-sway metrics best matched the non-linear function, that participant was categorized as exhibiting a stochastic-resonance effect in response to nGVS. With this approach, 11 of the 20 (55%) participants in the White-noise group and 6 of the 20 (30%) in the Pink-noise group were classified as displaying a stochastic-resonance effect in response to nGVS. Feature extraction All CoP trajectories were imported and processed with MATLAB (Version R2024a, MathWorks, 2024). After excluding individuals with missing data, the analysis included 19 participants in each group (Pink and White noise). The one subject who was removed from the Pink noise group had been previously classified as SR. To minimize the influence of dynamic adjustments associated with weight transfer, the first and the last 5 s of each trial were excluded from the analysis. The analysis was based on features extracted from the CoP trajectories (2,500 data points in each half of one trial) in the time and time-frequency domains. In addition to random noise, we derived seven time-domain features: (1) “Time” – the time for each CoP value during the 25-s intervals; (2) “CoPx” – CoP location in the side-to-side direction at each point in time; (3) “CoPy” – CoP location in the forward-backward direction at each point in time; (4) “Displacement” – the resultant x-y distance between two consecutive locations; (5) “Speed” – the rate of change in displacement; (6) “Area” – the area encompassed by the lines connecting two consecutive CoP location to the center of the coordinate system; and (7) “Sway-Area Rate” – the rate of change in the area encompassed by the lines connecting two consecutive CoP locations to the center of the coordinate system. The time-frequency features were identified with the Continuous Wavelet Transform (CWT) method using the default wavelet package in MATLAB. Features extracted in the time-frequency domain were measures of the spectral content of the CoP trajectory as a function of time. To achieve an adequate resolution in the time and frequency domains, the features comprised 84 bandwidths for each axis. The bandwidths were distributed logarithmically from the first spectral band (0.11–0.16 Hz) to the last (36.18–50.65 Hz). Classification algorithm Three machine learning models—decision tree, random forest, and K-nearest neighbors (KNN)—were evaluated. Among them, KNN, which has previously demonstrated its ability to distinguish features extracted from CoP trajectories (see Table 2 in Rahimi et al., 2025 ), was selected to classify CoP trajectories across the four conditions: (1) baseline (no noise), Pink noise, or White noise superimposed on five stimulus intensities (50%, 60%, 70%, 80%, or 90% of perceptual threshold); (2) baseline or the Pink-noise condition at all five intensities; (3) baseline or the White-noise condition at all five intensities; and (4) the additive influence of Pink or White noise on participants who either did (responders) or did not (non-responders) exhibit a stochastic-resonance effect in at least 2 of the 3 postural-sway measures. The models were optimized using GridSearchCV to identify the best hyperparameters, which are as follows: algorithm='auto', metric= 'manhattan', n_neighbors = 3, weights= 'distance'. All classifications were performed in Python Software Foundation (2024, Version 3.9). The relative importance of the time features was determined by permutation feature importance technique and sequential feature selection. The permutation method involved identifying the features that caused the most significant drop in model performance when shuffled (Khan et al. 2025 ), whereas the sequential approach involved assessing changes in model performance by iteratively adding or removing each feature (Gu et al. 2015 ). Additionally, the correlation-based feature selection method has been used to determine the best features in the time-frequency domain, particularly due to the large number of continuous wavelet transform outputs. Correlation-based feature selection is a method for identifying the most relevant features from a dataset, ensuring that selected features are highly correlated with the target variable while remaining weakly correlated with each other (Hall 1999 ). Subsequently, collinearity among the top features was examined using the Variance Inflation Factor (VIF). Values less than 1.02 in the time domain and 1.2 in the time-frequency domain ensured that highly correlated features were removed. To avoid data leakage caused by having data from individual participants in both splits, the datasets were shuffled and grouped by participant. The models were trained using 80% of the data and tested on the remaining 20%. We also applied a 10-fold cross-validation method to reduce the variance and produce more stable and reliable performance estimates (Kohavi 1995). 10-fold cross-validation splits the data into 10 parts, using each part as a test set while training on the remaining data, repeating this process 10 times, each fold serving as a test set once. This process evaluates model performance, reduces bias, and detects overfitting, with higher cross-validation results indicating the model is performing well and generalizing effectively to unseen data. The contribution of each feature to the predictions of a model was assessed with SHapley Additive exPlanation (SHAP) analysis. The SHAP framework, which is based on game theory, assigns an importance value to each feature for a given prediction, providing insight into the direction and magnitude of its impact on the model output (Lundberg et al. 2020 ). RESULTS The results assessed the capacity of the KNN model to discriminate among the CoP trajectories of healthy young adults while they stood upright on a firm surface with the eyes closed and received sub- and supra-threshold intensities of nGVS. Model performance Figure 2 illustrates the relative importance of the seven time-domain features extracted from the CoP trajectories compared with random noise. The three most important features determined by the permutation method were “Time”, “CoPy”, and “CoPx”. The two most important features determined by the correlation-based feature selection in the time-frequency domain were in a narrow band (0.11–0.16 Hz) in both the side-to-side (X) and forward-backward (Y) directions, which is consistent with previous reports (Sozzi et al. 2022 ). Model performance was quantified by how well the KNN algorithm was able to classify the CoP trajectory based on the extracted features in individual trials across the four experimental conditions described in the Methods. The performance of the model was evaluated with measures of accuracy (a ratio of correct prediction to total observations) and cross-validation. Table 1 lists the accuracy with which the algorithm could distinguish the CoP trajectories within each condition with three time-domain and two time-frequency domain features. Although, two features in the time-frequency domain (CTWx, CWTy) outperform the two features in the time domain (CoPx, CoPy; accuracay ranged from 44.3–77.1% across the four conditions), similar levels of accuracy were achieved with the set of three time-domain features (Time, CoPx, CoPy) and the two time-frequency features. High cross-validation accuracy with low standard deviations shown in Table 1 indicate that the model performed well and could generalize to unseen data. Table 1 Classification accuracy (%) and cross-validation accuracy achieved with the k-nearest neighbor algorithm applied to features extracted in the time and time-frequency domains across the four conditions. Time, CoPx, CoPy CWTx, CWTy Classification Cross-validation Classification Cross-validation Baseline vs. Pink vs. White 50% intensity 99.1% 99.3 ± 0.1% 98.7% 98.9 ± 0.1% 60% intensity 99.0% 99.3 ± 0.1% 98.4% 98.6 ± 0.1% 70% intensity 98.8% 99.1 ± 0.1% 98.4% 98.6 ± 0.1% 80% intensity 98.7% 99.0 ± 0.1% 98.8% 99.0 ± 0.1% 90% intensity 98.9% 99.2 ± 0.1% 98.9% 99.0 ± 0.1% Baseline vs. Pink intensities 96.4% 97.0 ± 0.1% 97.3% 97.7 ± 0.1% Baseline vs. White intensities 97.7% 98.2 ± 0.1% 96.6% 97.0 ± 0.1% SR vs. Non-SR Pink noise 97.9% 98.2 ± 0.1% 98.4% 98.7 ± 0.1% White noise 98.2% 98.6% ± 0.0% 97.3% 97.7 ± 0.1% CoP = center of pressure, CWT = continuous wavelet transform, x = side-to-side direction, y = forward-backward direction, SR = stochastic-resonance effect Figure 3 presents the confusion matrix for the categorization of participants into groups based on whether or not they exhibited a stochastic-resonance effect for at least 2 of the 3 postural-sway metrics in response to nGVS. The rows correspond to the true labels for the actual group, and the columns indicate the predicted group as identified with the KNN algorithm. The color intensity (dark to light) in each cell lists the percentage of times a specific group was identified by the algorithm. The diagonal of each matrix indicates the percentage of correct classifications. High values for correct classifications and low misclassifications between classes indicate the model performed well, and it accurately distinguished between different classes. The greatest misclassification, although minimal (~ 3%), occurred for the group in whom the stochastic-resonance effect was observed during the Pink-noise condition. SHAP analysis Figure 4 illustrates the average SHAP values in the time and time-frequency domains for the models that discriminated between the two groups of participants who exhibited a stochastic-resonance effect and those who did not during the Pink- and White-noise conditions. Greater average SHAP values indicate features that have a stronger influence on the predictive capacity of a model (Baptista et al. 2022 ). All three features in the time domain and the two features in the time-frequency domain (0.11–0.16 Hz in the x and y directions) contributed positively to the classification model during the two noise conditions. Although, the accuracy with which the two groups were classified was similar during the two noise conditions (Table 1 ), Fig. 4 indicates that the influence of the five variables indicated on the x-axis were greater during the White-noise condition (right panel) than the Pink-noise condition. This difference was greatest for the two time-frequency features (CWTx and CWTy). DISCUSSION The main findings of our study were that machine-learning models based on the KNN algorithm were able to distinguish among CoP trajectories in four conditions with a high level of accuracy. The four conditions differed in stimulus intensity and type of superimposed noise during nGVS and the response of the participants to the stimulation. In contrast to the conventional metrics used to characterize postural sway, our approach involved extracting features in the time and time-frequency domains from the entire set of values that comprised each CoP trajectory. The classification accuracy of the model indicates that there were unique differences in the CoP trajectories within each condition, including between participants who were categorized as exhibiting a stochastic-resonance effect and those who did not. According to the concept of stochastic resonance, the addition of noise to a stimulus that excites a sensory receptor can enhance weak signals generated by the receptor (McDonnell and Abbott, 2009 ; Nooristani et al. 2021 ). The most direct assessment of this effect is to measure the influence of noise added to a range of stimulus intensities on the threshold at which the receptor is perceived to be activated; so-called perceptual threshold. In the case of vestibular afferents, Stone et al. ( 2025 ) measured perceptual threshold as the shortest distance a seated individual could detect an imposed lateral displacement in the absence of vision. The presence of a stochastic-resonance effect was determined with a logistic regression machine-learning algorithm that identified the threshold as a function of nGVS amplitude. With the application of confidence-signal-detection thresholds, they found that the data for 6 of 10 participants were classified as exhibiting a stochastic-resonance effect. When this approach is applied to measures of postural sway, the assumption is that the noise-based modulation of afferent feedback can be detected as an adjustment in the selected outcome variable. The study from which we performed the secondary data analysis used this approach (Gavriilidou et al. 2025 ). They applied nGVS at intensities that were adjusted for each participant relative to the perceptual threshold for an evoked cutaneous sensation and compared the influence of superimposed Pink and White noise. At a group level, only one of the three postural-sway measures (mean CoP velocity) was influenced by nGVS. They found that mean CoP velocity increased with nGVS intensity during the Pink-noise condition, which indicated a destabilizing effect. At the individual level, most participants who exhibited the stochastic-resonance effect did so for all three of the postural-sway measures: 5/6 participants in the Pink-noise group and 6/10 in the White-noise group. These results are consistent with the broader literature on the association between postural-sway metrics and fall risk. In this field, postural control is often quantified with summary measures derived from CoP trajectories. For example, we used four of these measures in the current report: displacement, speed, area, and sway-area rate. None of these features was important enough to be included in the classification models (Fig. 2 ) and classification accuracy with these measures was substantially less than that achieved with the other two sets of features. Similarly, we previously reported that these measures were not included in machine-learning models that were able to classify CoP trajectories when participants stood on a firm or foam surface with eyes open or closed, when another group of participants performed four standing-balance tasks, and when older adults received transcutaneous electrical nerve stimulation while performing standard balance tasks (Rahimi et al. 2025 ). Moreover, Qiu and Xiong ( 2015 ) found that 3 out of 18 summary measures (trajectory RMS in the forward-backward direction, mean trajectory velocity, and phase-plane angle between the side-to-side and forward-backward directions) could distinguish between young and older adults, but that no single measure of postural sway derived from CoP trajectories could discriminate between older adults classified into two groups based on fall history. The literature is mixed on the relative influence of side-to-side and forward-backward features of the CoP trajectory on postural sway. Because nGVS tends to evoke a postural adjustment in the side-to-side direction when the head is facing forward (Fitzpatrick and Day, 2004), its effects are often examined in lateral directions (Galvan-Garza et al. 2018 ; Gavriilidou et al. 2025 ; Mulavara et al. 2011; Stone et al. 2025 ). However, nGVS appears to influence features in both the side-to-side and forward-backward directions (Inukai et al, 2018 ; Asslander et al. 2021). In our secondary analysis of the data from Gavriilidou et al. ( 2025 ), we found that the average SHAP values in the time- and time-frequency domains were significant in both directions and, therefore, contributed to the predictive capacity of a model. As shown in Fig. 4 , the CoP trajectories contained information in both directions that enabled the discrimination between participants who exhibited a stochastic-resonance effect and those who did not. Most studies on the influence of superimposed noise on the responsiveness of sensory receptors have typically added White noise to the stimulus (McLaren et al. 2023 ). Some evidence suggests that Pink noise, in which amplitude is inversely related to frequency, may be more effective in modulating afferent pathways and enhancing postural control (Brink et al. 2024 ; Yamagata et al. 2022 ). Nonetheless, Gavriilidou et al. ( 2025 ) found mixed effects of Pink noise at the group level; mean CoP velocity increased with nGVS intensity but there were no significant effects on either the root-mean-square value of the CoP displacement in the side-to-side direction or the area of an ellipse that enclosed 90% of the trajectory. At the individual level, however, our secondary analysis confirmed the original subjective ratings (Gavriilidou et al. 2025 ) and found that the influence of all five explanatory features in distinguishing between participants who exhibited a stochastic-resonance effect and those who did not was greater during the White-noise condition than the Pink-noise condition, especially the two time-frequency features (Fig. 4 ). Limitations The key finding from our secondary analysis was that the machine-learning models were able to distinguish between the CoP trajectories of participants who were categorized as exhibiting a stochastic-resonance effect or not during the application of nGVS. Moreover, the predictive capacity of the time and time-frequency features was greater during the White-noise condition. Although this comparison confirms that nGVS had a unique influence on these two groups of individuals, it provides no insight into the explicit adjustments elicited in the two groups of participants. Future work should explore this issue. In the current study, we extracted features derived from sections of CoP trajectories. Future studies should perform a classification analysis with neural network techniques applied to the entire CoP trajectory as input. Unfortunately, the relatively few participants in our study likely constrained the accuracy achievable with this approach. Moreover, the number of participants who exhibited a stochastic-resonance effect differed from those who did not (White-noise group: 11/20; Pink-noise group: 6/20). Future studies should attempt to enroll more similar numbers of participants in each group. CONCLUSION Our secondary analysis of previously published data demonstrated that machine-learning models using the KNN algorithm were able to distinguish among CoP trajectories in four conditions with a high level of accuracy. The explanatory features comprised three measures in the time domain and two in the time-frequency domain. The models were able to discriminate among the trajectories during conditions in which the stimulus intensity and type of superimposed noise during nGVS were varied between participants who either did or did not exhibit a stochastic-resonance effect. Moreover, the predictive capacity of the identified features was greater during the White-noise condition than when the nGVS stimulus was modulated with Pink noise. Declarations Authors’ contributions N.R., A. K., and R.M.E. conception and design of the secondary analysis; V.H. and A.G. performed the experiments; N.R and A.K. prepared figures; N.R., A.K., and R.M.E. drafted the manuscript; N.R., A.K., V.H., A.G., and R.M.E. edited and approved the final version of manuscript. Funding R.M.E. was partially supported by an award from the National Multiple Sclerosis Society in the USA (project RG-2206-39688). Data Availability Data will be made available on reasonable request. Conflicts of Interest None Ethic approval and consent to participate All participants received both verbal and written explanations of the study protocol and provided written informed consent before participating in the study. 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IEEE Access. doi: https://doi.org/10.1109/ACCESS.2025.3544625 Lundberg SM, Erion G, Chen H, et al. (2020) From local explanations to global understanding with explainable AI for trees. Nat Mach Intell 2:56-67 doi:https://doi.org/10.1038/s42256-019-0138-9 Matsugi A, Oku K, Mori N (2020) The effects o stochastic galvanic vestibular stimulation on body sway and muscle activity. Front Hum Neurosci 14:591571 https://doi.org/10.3389.fnhum.2020.591671 McDonnell MD, Abbott D (2009) What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Comput Biol 5:e1000348 https://doi.org/10.1371/journal.pcbi.1000348 McLaren R, Smith PF, Taylor RL, Niazi IK, Taylor D (2023) Scoping our noisy galvanic vestibular stimulation: a review of the parameters used to improve postural control. Front Neurosci 17:1156796 https://doi.org/10.3389/fnins.2023.1156796 Mitsutake T, Nakazono H, Shiozaki T, Fujta D, Sakamoto M (2024) Changes in vestibular-related responses to combined noisy galvanic vestibular stimulation and cerebellar direct current stimulation. Exp Brain Res 242:99-108 http://doi.org.10.1007/s00221-023-06731-5 Nooristani M, Bigras C, Lafontaine L, Bacon B-A, Maheu M, Champoux F (2021) Vestibular function modulates the impact of nGVS on postural control in older adults. J Neurophysiol 125: 489-495 http://doi.org/10.1152/jn.00512.2020 Osisanwo F, Akinsola J, Awodele O, Hinmikaiye J, Olakanmi O, Akinjobi J (2017) Supervised machine learning algorithms: classification and comparison. Int J Comput Trends Technol (IJCTT) 48:128-138 doi: http://dx.doi.org/10.14445/22312803/IJCTT-V48P126 Qiu H, Xiong S (2015) Center-of-pressure based postural sway measures: Reliability and ability to distinguish between age, fear of falling and fall history. Int J Ind Ergon 47:37-44 doi: https://doi.org/10.1016/j.ergon.2015.02.004 Rahimi N, Kamankesh A, Amiridis IG, Daneshgar S, Sahinis C, Hatzitaki V, Enoka RM (2025). Distinguishing among standing postures with machine learning-based classification algorithms. Exp Brain Res 243:3 Sozzi S, Do M-C, Schieppati M (2022) Vertical ground reaction force oscillation during standing on hard and compliant surfaces: The postural rhythm. Front Neurol 13:975752 doi: https://doi.org/10.3389/fneur.2022.975752 Stone T, Clark TK, Temple DR (2025) Noisy galvanic vestibular stimulation induces stochastic resonance in vestibular thresholds assessed efficiently using confidence reports. Exp Brain Res 243:34 http://doi.org/10.1007/s00221-024-06984-8 Yamagata M, Okada S, Tsujioka Y, Takayama A, Shiozawa N, Kimura T (2022) effects of subthreshold electrical stimulation with white noise, pink noise, and chaotic signals on postural control during quiet standing. Gait Posture 94:39-44 https://doi.org/10.1016/j.gaitpost.2022.02.023 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6306483","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":438807679,"identity":"4e585658-df6f-46c9-8509-8f76c618feb2","order_by":0,"name":"Negar Rahimi","email":"","orcid":"","institution":"University of Colorado Boulder","correspondingAuthor":false,"prefix":"","firstName":"Negar","middleName":"","lastName":"Rahimi","suffix":""},{"id":438807680,"identity":"9d098341-93bb-4041-96ec-28689457bef7","order_by":1,"name":"Vassilia Hatzitaki","email":"","orcid":"","institution":"Aristotle University of Thessaloniki","correspondingAuthor":false,"prefix":"","firstName":"Vassilia","middleName":"","lastName":"Hatzitaki","suffix":""},{"id":438807681,"identity":"39658cbd-52ee-43e3-9678-00310c7692be","order_by":2,"name":"Alireza Kamankesh","email":"","orcid":"","institution":"University of Colorado Boulder","correspondingAuthor":false,"prefix":"","firstName":"Alireza","middleName":"","lastName":"Kamankesh","suffix":""},{"id":438807682,"identity":"70e6b6b7-b95e-4891-a364-43fd4a7686c1","order_by":3,"name":"Alkistis Gavriilidou","email":"","orcid":"","institution":"Aristotle University of Thessaloniki","correspondingAuthor":false,"prefix":"","firstName":"Alkistis","middleName":"","lastName":"Gavriilidou","suffix":""},{"id":438807683,"identity":"0281f824-f9b3-4855-8e4f-401feb92ead3","order_by":4,"name":"Roger M. Enoka","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVRIiWNgGAWjYHACZgaGCgYGPhCTB0QcIErLGQYGNtK0MLaRooVfuvmwwc95dnJs7L0PP7ypYJDju5GAX4vknGPJib3bko3ZeI4bS845w2AsSUiLwY0c4wO82w4ktkmkMUjztjEkbiCkxR6o5eDfOWAtzL+BWuoJajGQyDFO5m0Aa2ED2ZJgQEiLxI20ZGOZYyC/HGOznHNGwnDmmQf4tfDPSD4s+abGTo6fvY35xpsKG3m+4wRswbCVNOWjYBSMglEwCrADAMI2PsvhRjgCAAAAAElFTkSuQmCC","orcid":"","institution":"University of Colorado Boulder","correspondingAuthor":true,"prefix":"","firstName":"Roger","middleName":"M.","lastName":"Enoka","suffix":""}],"badges":[],"createdAt":"2025-03-25 19:38:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6306483/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6306483/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80583233,"identity":"664f0680-eafb-4679-8117-afeb52c2c492","added_by":"auto","created_at":"2025-04-15 00:03:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":256907,"visible":true,"origin":"","legend":"\u003cp\u003eCenter-of-pressure (CoP) trajectories in the side-to-side and forward-backward directions at each point during a standing-balance task. Each row shows the trajectories for one participant when Pink noise was superimposed on three stimulus intensities (50%, 70%, and 90% of cutaneous perceptual threshold) of GVS during a 25-s trial. Darker colors represent the initial CoP locations at the start of each trial, whereas lighter colors indicate the final few seconds. The red and black circles mark the start and end locations of each trajectory. The top row indicates a participant whose adjustments in at least 2 of 3 balance metrics were categorized as exhibiting a stochastic-resonance effect, whereas the adjustments performed by the participant at the bottom did not meet this criterion. The data were obtained from Gavriilidou et al. (2025).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6306483/v1/d9248f0420078e4c3781e5fc.png"},{"id":80583232,"identity":"4038d82f-e5a9-40ea-bbbb-038ee153984f","added_by":"auto","created_at":"2025-04-15 00:03:41","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":79185,"visible":true,"origin":"","legend":"\u003cp\u003eFeature importance in the time domain. Each box plot indicates the feature importance scores of the 7 extracted features along with random noise across different intensities, with each data point corresponding to a specific intensity level (50%, 60%, 70%, 80%, and 90%). The boxes represent the median, 25th percentile, and 75th percentile of the feature importance scores.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6306483/v1/bf185571c4ec32d6ba2c0fc7.png"},{"id":80583246,"identity":"b3eceae3-01b0-4fd3-8aa2-01e9cd4dade6","added_by":"auto","created_at":"2025-04-15 00:03:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":91623,"visible":true,"origin":"","legend":"\u003cp\u003eConfusion matrix for the time (left column) and time-frequency (right column) features that distinguished between participants who exhibited a stochastic-resonance effect (SR) and those who did not (Non-SR) during the Pink-noise (top row) and the White-noise (bottom row) conditions. The categorization of participants was based on the adjustments in at least 2 of 3 balance metrics elicited by modulation of noisy galvanic vestibular stimulation (Gavriilidou et al. 2025). Rows represent the true labels corresponding to the group, whereas the columns indicate the predicted groupidentified by the KNN algorithm. The diagonal in each matrix indicates the sensitivity (the proportion of actual positives correctly identified) achieved by the algorithm. The color of each cell represents the percentage of times an instance was assigned to that group, with dark-to-light colors showing the relative percentage.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6306483/v1/6072472272234432b799e893.png"},{"id":80583696,"identity":"2b8b0ae3-f5cd-41fc-b341-ee1714b819e8","added_by":"auto","created_at":"2025-04-15 00:11:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":76170,"visible":true,"origin":"","legend":"\u003cp\u003eAverage SHAP values for the selected time and time-frequency features that distinguished between participants who exhibited a stochastic-resonance effect and those who did not during the Pink-noise condition (left) and the White-noise condition (right). The categorization of participants was based on the adjustments in at least 2 of 3 balance metrics elicited by modulation of noisy nGVS (Gavriilidou et al. 2025). All three features in the time domain (orange) and the two features in the time-frequency domain (green) contributed positively to the classification during the two noise conditions. The time-frequency variables “CWTx” and “CWTy” were limited to a narrow spectral band (0.11-0.16 Hz).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6306483/v1/4e3949e8ce9a50e7b8b1afba.png"},{"id":80584948,"identity":"fc4acc2d-064a-47be-94ac-196cebac3e96","added_by":"auto","created_at":"2025-04-15 00:27:46","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":926328,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6306483/v1/6eea89db-63c3-41c4-94c0-7592df64cb65.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Machine-learning classification of postural sway in young adults during colored noisy vestibular stimulation","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe concept of stochastic resonance asserts that a signal too weak to be detected by a sensor can be boosted by the addition of noise (Di Ponzio et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; McDonnell and Abbott, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; McLaren et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Nooristani et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This method has been used in the field of balance control to modulate the function of the vestibular system and associated networks (Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Mitsutake et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). It has been shown, for example, that the application of noisy galvanic stimulation at imperceptible intensities can enhance vestibular perception and improve several features of the center-of-pressure trajectories during upright standing (Inukai et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Matsugi et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, the effect varies across individuals, depending on such factors as stimulus characteristics, balance-control metric, age, and the functional status of the vestibular system (Assl\u0026auml;lander et al. 2021; Inukai et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Iwasaki et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Nooristani et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eCritically, the benefit of stochastic resonance is greatest at intermediate levels of added noise (Galvan-Garza et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Nooristani et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Stone et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The presence of a stochastic-resonance effect is typically determined by comparing the shape of a plot that shows the influence of added noise on an outcome variable across a range of stimulus intensities with a function (pseudo-bell-shaped curve) used to characterize the phenomenon (Galvan-Garza et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Stone et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The outcome variables can comprise measures of perceptual threshold (Galvan-Garza et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Stone et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) or balance-control metrics (Assl\u0026auml;lander et al. 2021; Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Nooristani et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Expert analysis of the plots has revealed that the proportion of individuals exhibiting a stochastic-resonance effect varies from 10\u0026ndash;78% across a broad range of study designs and outcome measures (Assl\u0026auml;lander et al. 2021; Galvan-Garza et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe current report comprises a secondary analysis of data that were published in Gavriilidou et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The purpose of that study was to evaluate the influence of two types of noisy galvanic vestibular stimulation (nGVS) on postural sway (CoP displacement) when young adults stood upright on a firm surface with feet together and eyes closed. nGVS intensity was set relative to the perceptual threshold of a cutaneous sensation elicited by the stimulation. At a group level, they found that the mean velocity of the CoP trajectory increased with stimulus intensity for the Pink-noise condition, but not for the White-noise condition or for either of the other two postural-sway metrics. Underlying these weak group effects, the responses exhibited by individual participants, as assessed by expert raters, were variable with 55% of the participants during the White-noise condition and 30% during the Pink-noise condition displaying a stochastic-resonance effect.\u003c/p\u003e \u003cp\u003eAn alternative approach to determine the influence of nGVS on postural sway is to apply machine-learning models to detect meaningful features within each condition (Daneshgar et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Dahiya et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Fadil et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Kamankesh et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Osisanwo et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Rahimi et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Stone et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The purpose of our study was to compare the accuracy of a machine-learning algorithm in distinguishing features extracted from CoP trajectories during upright standing when nGVS was applied at intensities relative to perceptual threshold. This approach used the information embedded in the time and time-frequency series of the CoP trajectories to assess their uniqueness within each of the four conditions. We hypothesized that distinct CoP trajectories could be identified due to the influence of stimulus intensity, type of superimposed noise, and the responsiveness of participants to the perturbation.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003eThis report is based on a secondary analysis of data that have already been published (Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). The purpose of that study was to evaluate the influence of nGVS on postural control when young adults stood upright on a firm surface with feet together and eyes closed. The study was performed at Aristotle University in Thessaloniki, Greece, and the protocol was approved by the Institutional Research Ethics and Ethics Committee (approval number 145/15.3.2023).\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eExperimental data\u003c/h2\u003e \u003cp\u003eIn a single experimental session, 40 healthy adults (25.1\u0026thinsp;\u0026plusmn;\u0026thinsp;5.6 years, 21 females) performed two tasks: (1) assessment of cutaneous perception threshold; and (2) measurement of CoP trajectories in the absence (baseline) and presence of nGVS added to seven stimulus intensities. Each participant was assigned to a group that received either White or Pink noise generated in LABVIEW (version 8.6, National Instruments) using the \u0026ldquo;Gaussian White Noise\u0026rdquo; or the \u0026ldquo;Inverse fNoises Waveform IV\u0026rdquo; functions, respectively. These signals were smoothed with a second-order Butterworth filter (\u0026le;\u0026thinsp;30 Hz). The signals had a zero mean, with the standard deviation (for white noise) and noise density (for pink noise) scaled to each of the 7 stimulus intensities: 50, 60, 70, 80, 90, 100, and 110% of the perceptual threshold.\u003c/p\u003e \u003cp\u003e Perceptual threshold was estimated as the lowest stimulus intensity at which the seated participants were able to detect a cutaneous sensation elicited by the applied stimulation. The stimulus was generated with a National Instruments device (NI PCI-6221) and delivered through a pair of rubber electrodes (PG980/2, Silicone Reusable Electrode 60x85 mm, Neurocare group AG, Germany) attached behind the ears with the cathode placed over the left mastoid. The stimulus was applied for 10 s at an increasing intensity in steps of 0.5 mA. The time between each stimulus intensity varied randomly within the range of 15 to 20 s. The average (mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation) current at which the perceptual threshold was detected was 410\u0026thinsp;\u0026plusmn;\u0026thinsp;120 \u0026micro;A for the White-noise group and 432\u0026thinsp;\u0026plusmn;\u0026thinsp;137 \u0026micro;A for the Pink-noise group.\u003c/p\u003e \u003cp\u003eThe standing balance task was performed on a force platform (model 6501, Bertec Corporation) that measured the three orthogonal components of the ground reaction force. Participants stood with feet together and eyes closed. Each trial lasted 60 s with nGVS being applied from 30 to 60 s during each of 7 trials. The order of the 7 levels of nGVS intensity was randomized across trials. Prior to performing the nGVS trials, participants completed one trial with no stimulation (baseline trial).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eData analysis\u003c/h2\u003e \u003cp\u003ePostural sway during each trial was quantified with three metrics derived from the CoP trajectory in the forward-backward and side-to-side directions (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The ground reaction force was digitized at 1000 Hz, down-sampled to 100 Hz, and low-pass filtered with a second-order Butterworth filter (cutoff frequency: 6 Hz). As a result of this processing, each 60-s trial comprised 6,000 data points in each of the two directions. The three metrics comprised: (1) the root-mean-square value of the CoP displacement in the side-to-side direction; (2) the mean CoP velocity in the side-to-side direction; and (3) the area of an ellipse that enclosed 90% of the trajectory. These metrics were calculated for the period of no nGVS (5\u0026ndash;30 s) and the interval during which nGVS was applied (30\u0026ndash;55 s), which in each instance involved reducing the 2,500 data points to a single value. These metrics were then used to categorize individual CoP trajectories as exhibiting stochastic resonance or not.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe influence of nGVS on the postural-sway metrics was examined by Gavriilidou et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) at both the group and individual levels. In the current report, we focus on the results obtained at the individual level. The analysis examined the influence of each type of nGVS (White or Pink noise) on the relative changes in the postural-sway metrics across the 7 stimulus intensities. Specifically, a reduction in the normalized value of a metric at intermediate stimulus intensities (characteristic Bell-shaped curve) was interpreted as evidence of a stochastic-resonance effect. Three experts examined the plots and independently rated the data for each condition (type of noise, stimulus intensity, and postural-sway metric) as being best fit with a linear function or the characteristic Bell-shaped curve (Galvan Garza et al. 2018; Stone et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). When two or three raters deemed that the data for at least 2 of the 3 postural-sway metrics best matched the non-linear function, that participant was categorized as exhibiting a stochastic-resonance effect in response to nGVS. With this approach, 11 of the 20 (55%) participants in the White-noise group and 6 of the 20 (30%) in the Pink-noise group were classified as displaying a stochastic-resonance effect in response to nGVS.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eFeature extraction\u003c/h3\u003e\n\u003cp\u003eAll CoP trajectories were imported and processed with MATLAB (Version R2024a, MathWorks, 2024). After excluding individuals with missing data, the analysis included 19 participants in each group (Pink and White noise). The one subject who was removed from the Pink noise group had been previously classified as SR. To minimize the influence of dynamic adjustments associated with weight transfer, the first and the last 5 s of each trial were excluded from the analysis.\u003c/p\u003e \u003cp\u003eThe analysis was based on features extracted from the CoP trajectories (2,500 data points in each half of one trial) in the time and time-frequency domains. In addition to random noise, we derived seven time-domain features: (1) \u0026ldquo;Time\u0026rdquo; \u0026ndash; the time for each CoP value during the 25-s intervals; (2) \u0026ldquo;CoPx\u0026rdquo; \u0026ndash; CoP location in the side-to-side direction at each point in time; (3) \u0026ldquo;CoPy\u0026rdquo; \u0026ndash; CoP location in the forward-backward direction at each point in time; (4) \u0026ldquo;Displacement\u0026rdquo; \u0026ndash; the resultant \u003cem\u003ex-y\u003c/em\u003e distance between two consecutive locations; (5) \u0026ldquo;Speed\u0026rdquo; \u0026ndash; the rate of change in displacement; (6) \u0026ldquo;Area\u0026rdquo; \u0026ndash; the area encompassed by the lines connecting two consecutive CoP location to the center of the coordinate system; and (7) \u0026ldquo;Sway-Area Rate\u0026rdquo; \u0026ndash; the rate of change in the area encompassed by the lines connecting two consecutive CoP locations to the center of the coordinate system.\u003c/p\u003e \u003cp\u003eThe time-frequency features were identified with the Continuous Wavelet Transform (CWT) method using the default wavelet package in MATLAB. Features extracted in the time-frequency domain were measures of the spectral content of the CoP trajectory as a function of time. To achieve an adequate resolution in the time and frequency domains, the features comprised 84 bandwidths for each axis. The bandwidths were distributed logarithmically from the first spectral band (0.11\u0026ndash;0.16 Hz) to the last (36.18\u0026ndash;50.65 Hz).\u003c/p\u003e\n\u003ch3\u003eClassification algorithm\u003c/h3\u003e\n\u003cp\u003eThree machine learning models\u0026mdash;decision tree, random forest, and K-nearest neighbors (KNN)\u0026mdash;were evaluated. Among them, KNN, which has previously demonstrated its ability to distinguish features extracted from CoP trajectories (see Table\u0026nbsp;2 in Rahimi et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), was selected to classify CoP trajectories across the four conditions: (1) baseline (no noise), Pink noise, or White noise superimposed on five stimulus intensities (50%, 60%, 70%, 80%, or 90% of perceptual threshold); (2) baseline or the Pink-noise condition at all five intensities; (3) baseline or the White-noise condition at all five intensities; and (4) the additive influence of Pink or White noise on participants who either did (responders) or did not (non-responders) exhibit a stochastic-resonance effect in at least 2 of the 3 postural-sway measures. The models were optimized using GridSearchCV to identify the best hyperparameters, which are as follows: algorithm='auto', metric= 'manhattan', n_neighbors\u0026thinsp;=\u0026thinsp;3, weights= 'distance'. All classifications were performed in Python Software Foundation (2024, Version 3.9).\u003c/p\u003e \u003cp\u003eThe relative importance of the time features was determined by permutation feature importance technique and sequential feature selection. The permutation method involved identifying the features that caused the most significant drop in model performance when shuffled (Khan et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), whereas the sequential approach involved assessing changes in model performance by iteratively adding or removing each feature (Gu et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Additionally, the correlation-based feature selection method has been used to determine the best features in the time-frequency domain, particularly due to the large number of continuous wavelet transform outputs. Correlation-based feature selection is a method for identifying the most relevant features from a dataset, ensuring that selected features are highly correlated with the target variable while remaining weakly correlated with each other (Hall \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1999\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSubsequently, collinearity among the top features was examined using the Variance Inflation Factor (VIF). Values less than 1.02 in the time domain and 1.2 in the time-frequency domain ensured that highly correlated features were removed.\u003c/p\u003e \u003cp\u003eTo avoid data leakage caused by having data from individual participants in both splits, the datasets were shuffled and grouped by participant. The models were trained using 80% of the data and tested on the remaining 20%. We also applied a 10-fold cross-validation method to reduce the variance and produce more stable and reliable performance estimates (Kohavi 1995). 10-fold cross-validation splits the data into 10 parts, using each part as a test set while training on the remaining data, repeating this process 10 times, each fold serving as a test set once. This process evaluates model performance, reduces bias, and detects overfitting, with higher cross-validation results indicating the model is performing well and generalizing effectively to unseen data.\u003c/p\u003e \u003cp\u003eThe contribution of each feature to the predictions of a model was assessed with SHapley Additive exPlanation (SHAP) analysis. The SHAP framework, which is based on game theory, assigns an importance value to each feature for a given prediction, providing insight into the direction and magnitude of its impact on the model output (Lundberg et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eThe results assessed the capacity of the KNN model to discriminate among the CoP trajectories of healthy young adults while they stood upright on a firm surface with the eyes closed and received sub- and supra-threshold intensities of nGVS.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eModel performance\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the relative importance of the seven time-domain features extracted from the CoP trajectories compared with random noise. The three most important features determined by the permutation method were \u0026ldquo;Time\u0026rdquo;, \u0026ldquo;CoPy\u0026rdquo;, and \u0026ldquo;CoPx\u0026rdquo;. The two most important features determined by the correlation-based feature selection in the time-frequency domain were in a narrow band (0.11\u0026ndash;0.16 Hz) in both the side-to-side (X) and forward-backward (Y) directions, which is consistent with previous reports (Sozzi et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eModel performance was quantified by how well the KNN algorithm was able to classify the CoP trajectory based on the extracted features in individual trials across the four experimental conditions described in the Methods. The performance of the model was evaluated with measures of accuracy (a ratio of correct prediction to total observations) and cross-validation. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists the accuracy with which the algorithm could distinguish the CoP trajectories within each condition with three time-domain and two time-frequency domain features. Although, two features in the time-frequency domain (CTWx, CWTy) outperform the two features in the time domain (CoPx, CoPy; accuracay ranged from 44.3\u0026ndash;77.1% across the four conditions), similar levels of accuracy were achieved with the set of three time-domain features (Time, CoPx, CoPy) and the two time-frequency features. High cross-validation accuracy with low standard deviations shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e indicate that the model performed well and could generalize to unseen data.\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\u003eClassification accuracy (%) and cross-validation accuracy achieved with the k-nearest neighbor algorithm applied to features extracted in the time and time-frequency domains across the four conditions.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eTime, CoPx, CoPy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eCWTx, CWTy\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClassification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCross-validation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eClassification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCross-validation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline vs. Pink vs. White\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50% intensity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e99.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e99.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e98.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e60% intensity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e99.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e99.3\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e98.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e70% intensity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e98.8%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e99.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e98.6\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e80% intensity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e98.7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e99.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.8%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e99.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e90% intensity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e98.9%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e99.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.9%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e99.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline vs. Pink intensities\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e96.4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e97.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e97.3%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e97.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline vs. White intensities\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e97.7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e96.6%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e97.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSR vs. Non-SR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePink noise\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e97.9%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98.2\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e98.4%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e98.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWhite noise\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e98.2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e98.6% \u0026plusmn; 0.0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e97.3%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e97.7\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eCoP\u0026thinsp;=\u0026thinsp;center of pressure, CWT\u0026thinsp;=\u0026thinsp;continuous wavelet transform, x\u0026thinsp;=\u0026thinsp;side-to-side direction, y\u0026thinsp;=\u0026thinsp;forward-backward direction, SR\u0026thinsp;=\u0026thinsp;stochastic-resonance effect\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the confusion matrix for the categorization of participants into groups based on whether or not they exhibited a stochastic-resonance effect for at least 2 of the 3 postural-sway metrics in response to nGVS. The rows correspond to the true labels for the actual group, and the columns indicate the predicted group as identified with the KNN algorithm. The color intensity (dark to light) in each cell lists the percentage of times a specific group was identified by the algorithm. The diagonal of each matrix indicates the percentage of correct classifications. High values for correct classifications and low misclassifications between classes indicate the model performed well, and it accurately distinguished between different classes. The greatest misclassification, although minimal (~\u0026thinsp;3%), occurred for the group in whom the stochastic-resonance effect was observed during the Pink-noise condition.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSHAP analysis\u003c/h3\u003e\n\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the average SHAP values in the time and time-frequency domains for the models that discriminated between the two groups of participants who exhibited a stochastic-resonance effect and those who did not during the Pink- and White-noise conditions. Greater average SHAP values indicate features that have a stronger influence on the predictive capacity of a model (Baptista et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). All three features in the time domain and the two features in the time-frequency domain (0.11\u0026ndash;0.16 Hz in the x and y directions) contributed positively to the classification model during the two noise conditions. Although, the accuracy with which the two groups were classified was similar during the two noise conditions (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e indicates that the influence of the five variables indicated on the x-axis were greater during the White-noise condition (right panel) than the Pink-noise condition. This difference was greatest for the two time-frequency features (CWTx and CWTy).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThe main findings of our study were that machine-learning models based on the KNN algorithm were able to distinguish among CoP trajectories in four conditions with a high level of accuracy. The four conditions differed in stimulus intensity and type of superimposed noise during nGVS and the response of the participants to the stimulation. In contrast to the conventional metrics used to characterize postural sway, our approach involved extracting features in the time and time-frequency domains from the entire set of values that comprised each CoP trajectory. The classification accuracy of the model indicates that there were unique differences in the CoP trajectories within each condition, including between participants who were categorized as exhibiting a stochastic-resonance effect and those who did not.\u003c/p\u003e \u003cp\u003eAccording to the concept of stochastic resonance, the addition of noise to a stimulus that excites a sensory receptor can enhance weak signals generated by the receptor (McDonnell and Abbott, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Nooristani et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The most direct assessment of this effect is to measure the influence of noise added to a range of stimulus intensities on the threshold at which the receptor is perceived to be activated; so-called perceptual threshold. In the case of vestibular afferents, Stone et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) measured perceptual threshold as the shortest distance a seated individual could detect an imposed lateral displacement in the absence of vision. The presence of a stochastic-resonance effect was determined with a logistic regression machine-learning algorithm that identified the threshold as a function of nGVS amplitude. With the application of confidence-signal-detection thresholds, they found that the data for 6 of 10 participants were classified as exhibiting a stochastic-resonance effect.\u003c/p\u003e \u003cp\u003eWhen this approach is applied to measures of postural sway, the assumption is that the noise-based modulation of afferent feedback can be detected as an adjustment in the selected outcome variable. The study from which we performed the secondary data analysis used this approach (Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). They applied nGVS at intensities that were adjusted for each participant relative to the perceptual threshold for an evoked cutaneous sensation and compared the influence of superimposed Pink and White noise. At a group level, only one of the three postural-sway measures (mean CoP velocity) was influenced by nGVS. They found that mean CoP velocity increased with nGVS intensity during the Pink-noise condition, which indicated a destabilizing effect. At the individual level, most participants who exhibited the stochastic-resonance effect did so for all three of the postural-sway measures: 5/6 participants in the Pink-noise group and 6/10 in the White-noise group.\u003c/p\u003e \u003cp\u003eThese results are consistent with the broader literature on the association between postural-sway metrics and fall risk. In this field, postural control is often quantified with summary measures derived from CoP trajectories. For example, we used four of these measures in the current report: displacement, speed, area, and sway-area rate. None of these features was important enough to be included in the classification models (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and classification accuracy with these measures was substantially less than that achieved with the other two sets of features. Similarly, we previously reported that these measures were not included in machine-learning models that were able to classify CoP trajectories when participants stood on a firm or foam surface with eyes open or closed, when another group of participants performed four standing-balance tasks, and when older adults received transcutaneous electrical nerve stimulation while performing standard balance tasks (Rahimi et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Moreover, Qiu and Xiong (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) found that 3 out of 18 summary measures (trajectory RMS in the forward-backward direction, mean trajectory velocity, and phase-plane angle between the side-to-side and forward-backward directions) could distinguish between young and older adults, but that no single measure of postural sway derived from CoP trajectories could discriminate between older adults classified into two groups based on fall history.\u003c/p\u003e \u003cp\u003eThe literature is mixed on the relative influence of side-to-side and forward-backward features of the CoP trajectory on postural sway. Because nGVS tends to evoke a postural adjustment in the side-to-side direction when the head is facing forward (Fitzpatrick and Day, 2004), its effects are often examined in lateral directions (Galvan-Garza et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Mulavara et al. 2011; Stone et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). However, nGVS appears to influence features in both the side-to-side and forward-backward directions (Inukai et al, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Asslander et al. 2021). In our secondary analysis of the data from Gavriilidou et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), we found that the average SHAP values in the time- and time-frequency domains were significant in both directions and, therefore, contributed to the predictive capacity of a model. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the CoP trajectories contained information in both directions that enabled the discrimination between participants who exhibited a stochastic-resonance effect and those who did not.\u003c/p\u003e \u003cp\u003eMost studies on the influence of superimposed noise on the responsiveness of sensory receptors have typically added White noise to the stimulus (McLaren et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Some evidence suggests that Pink noise, in which amplitude is inversely related to frequency, may be more effective in modulating afferent pathways and enhancing postural control (Brink et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Yamagata et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Nonetheless, Gavriilidou et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) found mixed effects of Pink noise at the group level; mean CoP velocity increased with nGVS intensity but there were no significant effects on either the root-mean-square value of the CoP displacement in the side-to-side direction or the area of an ellipse that enclosed 90% of the trajectory. At the individual level, however, our secondary analysis confirmed the original subjective ratings (Gavriilidou et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) and found that the influence of all five explanatory features in distinguishing between participants who exhibited a stochastic-resonance effect and those who did not was greater during the White-noise condition than the Pink-noise condition, especially the two time-frequency features (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eLimitations\u003c/h2\u003e \u003cp\u003eThe key finding from our secondary analysis was that the machine-learning models were able to distinguish between the CoP trajectories of participants who were categorized as exhibiting a stochastic-resonance effect or not during the application of nGVS. Moreover, the predictive capacity of the time and time-frequency features was greater during the White-noise condition. Although this comparison confirms that nGVS had a unique influence on these two groups of individuals, it provides no insight into the explicit adjustments elicited in the two groups of participants. Future work should explore this issue.\u003c/p\u003e \u003cp\u003eIn the current study, we extracted features derived from sections of CoP trajectories. Future studies should perform a classification analysis with neural network techniques applied to the entire CoP trajectory as input. Unfortunately, the relatively few participants in our study likely constrained the accuracy achievable with this approach. Moreover, the number of participants who exhibited a stochastic-resonance effect differed from those who did not (White-noise group: 11/20; Pink-noise group: 6/20). Future studies should attempt to enroll more similar numbers of participants in each group.\u003c/p\u003e \u003c/div\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eOur secondary analysis of previously published data demonstrated that machine-learning models using the KNN algorithm were able to distinguish among CoP trajectories in four conditions with a high level of accuracy. The explanatory features comprised three measures in the time domain and two in the time-frequency domain. The models were able to discriminate among the trajectories during conditions in which the stimulus intensity and type of superimposed noise during nGVS were varied between participants who either did or did not exhibit a stochastic-resonance effect. Moreover, the predictive capacity of the identified features was greater during the White-noise condition than when the nGVS stimulus was modulated with Pink noise.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u0026nbsp;\u003c/strong\u003eN.R., A. K., and R.M.E. conception and design of the secondary analysis; V.H. and A.G. performed the experiments; N.R and A.K. prepared figures; N.R., A.K., and R.M.E. drafted the manuscript; N.R., A.K., V.H., A.G., and R.M.E. edited and approved the final version of manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u0026nbsp;\u003c/strong\u003eR.M.E. was partially supported by an award from the National Multiple Sclerosis Society in the USA (project RG-2206-39688).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u0026nbsp;\u003c/strong\u003eData will be made available on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest\u0026nbsp;\u003c/strong\u003eNone\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthic approval and consent to participate\u0026nbsp;\u003c/strong\u003eAll participants received both verbal and written explanations of the study protocol and provided written informed consent before participating in the study. The protocol was approved by the Institutional Research Ethics and Ethics Committee of Aristotle University in Thessaloniki, Greece (approval number 145/15.3.2023).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication\u0026nbsp;\u003c/strong\u003eThe authors consent to the publication of this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAssl\u0026auml;nder L, Giboin LS, Gruber M, Schniep R, Wuehr M (2021) No evidence for stochastic resonance effects on standing balance when applying noisy galvanic vestibular stimulation in young healthy adults. Sci Rep 11:12327 http://doi.org/10.1038/s41589-021-91808 \u003c/li\u003e\n\u003cli\u003eBaptista ML, Goebel K, Henriques EM (2022) Relation between prognostics predictor evaluation metrics and local interpretability SHAP values. 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(2020) From local explanations to global understanding with explainable AI for trees. Nat Mach Intell 2:56-67 doi:https://doi.org/10.1038/s42256-019-0138-9\u003c/li\u003e\n\u003cli\u003eMatsugi A, Oku K, Mori N (2020) The effects o stochastic galvanic vestibular stimulation on body sway and muscle activity. Front Hum Neurosci 14:591571 https://doi.org/10.3389.fnhum.2020.591671 \u003c/li\u003e\n\u003cli\u003eMcDonnell MD, Abbott D (2009) What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Comput Biol 5:e1000348 https://doi.org/10.1371/journal.pcbi.1000348\u003c/li\u003e\n\u003cli\u003eMcLaren R, Smith PF, Taylor RL, Niazi IK, Taylor D (2023) Scoping our noisy galvanic vestibular stimulation: a review of the parameters used to improve postural control. 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Int J Comput Trends Technol (IJCTT) 48:128-138 doi: http://dx.doi.org/10.14445/22312803/IJCTT-V48P126\u003c/li\u003e\n\u003cli\u003eQiu H, Xiong S (2015) Center-of-pressure based postural sway measures: Reliability and ability to distinguish between age, fear of falling and fall history. Int J Ind Ergon 47:37-44 doi: https://doi.org/10.1016/j.ergon.2015.02.004\u003c/li\u003e\n\u003cli\u003eRahimi N, Kamankesh A, Amiridis IG, Daneshgar S, Sahinis C, Hatzitaki V, Enoka RM (2025). Distinguishing among standing postures with machine learning-based classification algorithms. Exp Brain Res 243:3 \u003c/li\u003e\n\u003cli\u003eSozzi S, Do M-C, Schieppati M (2022) Vertical ground reaction force oscillation during standing on hard and compliant surfaces: The postural rhythm. Front Neurol 13:975752 doi: https://doi.org/10.3389/fneur.2022.975752\u003c/li\u003e\n\u003cli\u003eStone T, Clark TK, Temple DR (2025) Noisy galvanic vestibular stimulation induces stochastic resonance in vestibular thresholds assessed efficiently using confidence reports. Exp Brain Res 243:34 http://doi.org/10.1007/s00221-024-06984-8 \u003c/li\u003e\n\u003cli\u003eYamagata M, Okada S, Tsujioka Y, Takayama A, Shiozawa N, Kimura T (2022) effects of subthreshold electrical stimulation with white noise, pink noise, and chaotic signals on postural control during quiet standing. Gait Posture 94:39-44 https://doi.org/10.1016/j.gaitpost.2022.02.023\u003c/li\u003e\n\u003c/ol\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":"K-Nearest Neighbor Algorithm, Standing Posture, Vestibular Stimulation, Colored Noise, Stochastic Resonance, Continuous Wavelet Transform","lastPublishedDoi":"10.21203/rs.3.rs-6306483/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6306483/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe compared the accuracy with which a machine-learning algorithm could distinguish among center-of-pressure (CoP) trajectories during upright standing when noisy galvanic vestibular stimulation (nGVS) was applied at intensities relative to the perceptual threshold. This report comprises a secondary analysis of data published in Gavriilidou et al. (2025). The k-nearest neighbor (KNN) algorithm was used to classify CoP trajectories recorded while young healthy adults stood on a firm surface with feet together and eyes closed. From 7 variables in the time domain and 84 bandwidths in each axis in the time-frequency domain, the three most important features in the time domain and two in the time-frequency domain were selected by permutation feature importance and correlation-based feature selection techniques, respectively. Models were developed to determine classification accuracy in four conditions derived from combinations of stimulus intensity (% perceptual threshold), type of superimposed noise (Pink or White), and the responsiveness of participants to the perturbation. Classification accuracy was \u0026gt;96% in all four conditions, which indicates that the CoP trajectories were unique at each level within the four conditions. Critically, the machine-learning model was able to discriminate the features extracted from CoP trajectories for participants who either did or did not exhibit a stochastic-resonance effect in response to nGVS. Moreover, SHapley Additive exPlanation analysis found that the contribution of the five extracted features in classifying these two groups of participants was greater during the White-noise condition. These results indicate that nGVS had unique effects on CoP trajectories within each of the four conditions.\u003c/p\u003e","manuscriptTitle":"Machine-learning classification of postural sway in young adults during colored noisy vestibular stimulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-15 00:03:37","doi":"10.21203/rs.3.rs-6306483/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":"216cc833-8742-4435-8252-12f759a493fe","owner":[],"postedDate":"April 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-04-15T00:03:39+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-15 00:03:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6306483","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6306483","identity":"rs-6306483","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}