{"paper_id":"0720bf98-51da-4bad-abdb-c1ef3e5a9631","body_text":"Multivariate classification\nmodels are commonly employed across\nmany scientific fields, such as food science, medical diagnostics,\nforensic analysis, microbiological studies, and fuel research, among\nothers. \n − \n \n \n \n  In analytical chemistry, the aim of classification is to build categories,\ni.e., classes based on data acquired to characterize samples through\na set of variables.\nThe term “class” denotes a\ngroup of samples that\nshare similar features.  Classification\nmodels are an important group of pattern recognition tools often applied\nin two-class or multiclass classifiers. Historically, they were the\nfirst multivariate models introduced and applied to qualitative analyses\nin pattern recognition. Their use has gained strength as relevant\nsoftware has become more commercially available, seemingly providing\nbetter results compared with other models.  Models such as Linear Discriminant Analysis (LDA), Quadratic Discriminant\nAnalysis (QDA), Partial Least Squares Discriminant Analysis (PLS-DA),\nk-Nearest Neighbors (k-NN), and Support Vector Machines (SVM), among\nothers, are known discriminant models.\nClass modeling (CM) or one-class classifier (OCC) models are\nan\nimportant set of models that answer the following general question:\n“can object O, declared of class A, really belong to class\nA?”  For this, it is assumed that\nthe term “class” denotes a set of samples that share\nsimilar features or attributes.  Therefore,\nthe class model is constructed using samples that undoubtedly belong\nto the target class, characterized by chemical, physical, and other\nrelevant variables.\nSensitivity\nand specificity are parameters that characterize a\nclass model. Sensitivity measures the percentage of correct positive\ndecisions (i.e., the ability to correctly identified true positives,\nthereby minimizing type I errors), while specificity measures the\ncomplementary percentage of correct negative decisions, thereby reducing\ntype II errors.  Models such as Soft Independent\nModeling of Class Analogy (SIMCA) and two of its variants, Alternative\nSIMCA (Alt-SIMCA) and Data Driven SIMCA (DD-SIMCA), as well as Unequal\nClass Spaces (UNEQ), Potential Functions (PF), One-Class Support Vector\nMachines (OC-SVM), and One-Class Partial Least Squares (OCPLS), among\nothers, are some examples of class modeling models.\nDiscriminant analysis is composed of binary (conventional)\nand\nmulticlass discrimination.  The main distinction\nbetween discriminant binary and class modeling is that discriminant\nbinary requires at least two classes to define the optimal boundary\nseparating objects belonging to different classes. In contrast, class\nmodeling can be approached in asymmetric cases, where a single class\nis represented in the training set, or in scenarios where only one\nclass needs to be modeled.  Furthermore,\nan enclosed class space is defined according to predetermined confidence\nlevels, enabling the verification of compliance.  When an object is tested against multiple modeled classes,\nit may be assigned to more than one class.  To improve the classification models, variable selection algorithms\ncan be applied to the data sets.\nVariable selection algorithms\nare useful tools to find specific\nspectral markers associated with class separation. These algorithms\nenable the extraction of features from dominant spectral bands, effectively\nreducing the high redundancy and strong collinearity. By selecting\nrepresentative variables, they allow grouping and replacement of the\noriginal set of variables, leading to a more concise, simple, and\ninformative model, along with reducing the noise caused by irrelevant\nvariables. \n ,\nVarious types of variable\nselection strategies are employed in\ndata sets, typically classified into three main groups: filter approaches,\nwrapper approaches, and embedded approaches. Filter approaches evaluate\nvariable performance based on inherent properties prior to model building,\ngenerally by defining a ranking criterion and applying a threshold.\nSome examples include Variable Importance in Projection (VIP) and\nSelectivity Ratio (SR). Wrapper approaches, on the other hand, perform\nfeature selection iteratively, as seen in strategies such as the Genetic\nAlgorithm (GA). Lastly, embedded approaches integrate variable selection\nwithin the model development process, including models like Principal\nComponent Analysis (PCA) and Partial Least Squares (PLS) regression. \n ,\nHerein, a new variable selection approach for class modeling\nis\nreported. This approach is a modification of the GA for discriminant\nanalysis applied to a single class. This can be a useful approach\nto enhance class discrimination and spectral interpretability of complex\ndata sets for authenticity applications or for modeling specific target\nclasses.\n\nThe Data Driven Soft Independent\nModeling of Class Analogy (DD-SIMCA) is a variant of SIMCA, one of\nthe most widely used one-class classification models in chemometrics. \n , , \n  A comprehensive description of\nthe DD-SIMCA theory can be found elsewhere. \n ,\nDD-SIMCA is based on the decomposition of preprocessed data.  In this approach, PCA is applied to model the\ntarget class using the training data matrix  X  ( I  ×  J ), as described in  eq  \n : \n 1 \n X = T P T + E \n where  X  is the preprocessed spectral\ndata matrix of size ( I  ×  J ),\nwhere  I  is the number of objects and  J  the number of variables;  T  is the scores matrix of\nsize ( I  ×  A ), where A is the\nnumber of principal components;  P  is the loadings matrix\nof size ( J  ×  A ); and  E  ( I  ×  J ) represents\nthe residuals matrix. The superscript T denotes the matrix transpose.\nBased on the PCA results, the score distance (SD),  h \n \n i \n , and the orthogonal distance (OD),\nν \n i \n , are calculated. The SD is defined\nas the squared Mahalanobis distance and reflects how far the projection\nof sample  i  lies from the origin of the principal\ncomponent (PC) space. Although the Mahalanobis distance typically\naccounts for pairwise covariance between variables, this is not an\nissue in this context, as PCA scores are orthogonal by design.\nThe OD is defined as the squared Euclidean distance between sample  i  and the score subspace; that is, it represents how far\nthe original data point is from its corresponding projection in the\nPC space.\nThe SD ( h \n \n i \n ) and OD\n( v \n \n i \n ) can be calculated\nusing  eqs  \n  and  , respectively: \n 2 \n h i = ∑ a = 1 A t i a 2 λ a \n \n \n 3 \n v i = ∑ j = 1 J e i j 2 \n where λ \n a \n  =  t \n \n a \n \n T \n t \n \n a \n  is the eigenvalue corresponding to component  a ,\nrepresenting the sum of the squared score values for that component\n( t \n \n a \n ); and  e  is the residual. In possession of the distances, the distance plot\ncan be plotted as  h / h \n 0  vs  v / v \n 0  or log  h / h \n 0  vs log  v / v \n 0 . The total distance is then calculated\nby  eq  \n : \n 4 \n c = N h h h 0 + N v v v 0 ∝ X 2 ( N h + N v ) \n where parameters  v \n 0  and  h \n 0  are the scaling factors, and  N \n \n h \n  and  N \n \n v \n  represent the respective degrees of freedom\n(DoF). These parameters are unknown  a priori  and\ncan be estimated using a data driven approach. \n ,\nThe acceptance area (or decision threshold) for the target\nclass\nis defined based on a predefined type I error rate, α. The acceptance\ncondition is given by \n 5 \n c ≤ c crit ( α ) \n where \n 6 \n c crit = X 2 ( 1 − α , N h + N v ) \n \n X \n 2  is the (1 –\nα) quartile of the chi-squared distribution with  N \n \n h \n  +  N \n \n v \n  degrees of freedom. \n , \n  After this step, the\nmodel is finalized and is ready for the classification of new data\nsamples. It can be represented by an acceptance area in the orthogonal\nvs score distance space, also known as the acceptance plot, defined\nby the given α value. The α value specifies the type I\nerror. Each sample in the training set can be characterized as regular,\nextreme, or outlier, depending on its location in the acceptance plot.\nA regular sample is one that is well described by the model and assigned\nto the target class. An extreme sample lies at the boundary of the\nacceptance area and may still belong to the target class but with\nhigher variability. An alien sample, considered an outlier, is not\nattributed to the target class and is assumed to belong to an alternative\nmeta-class. \n , \n  The second cutoff level is defined\nas the outlier boundary, constructed based on a specified γ\nvalue. This value represents the probability that at least one regular\nobject from the training set will be erroneously classified as an\noutlier. Unlike the acceptance area, the outlier boundary depends\non the size of the training set. The value for γ is 0.01.\nThe extreme plot and sensitivity plot can help assess the quality\nof classification models and support the selection of the optimal\nnumber of PCs. \n ,\nThe classification results\nare shown in the acceptance plot. In\naddition, the value of the type II error (β), which represents\nthe rate of incorrect acceptance of alien samples as target class\nobjects, is calculated. A reverse evaluation is also possible, in\nwhich a specific type I error (α) corresponds to a given value\nof the type II error (β).\nThe One-Class Partial Least\nSquares (OCPLS) classifier is a class modeling (CM) approach based\non Partial Least Squares (PLS), offering performance comparable to\nthat of SIMCA. \n , \n  However, data analysis may sometimes\ninvolve outliers and nonlinear contaminated data sets, which can lead\nto failures and bias in parameter estimation.  To address these issues, variants such as the ordinary OCPLS, the\nnonlinear Gaussian Radial Basis Function (RBF or GRBF)-OCPLS, and\nthe robust OCPLS based on partial robust M-regression (PRM) have been\nproposed in the literature. \n ,\nThe OCPLS model\nis constructed as a special case of PLS regression, assuming that  X  ( m  ×  n ) contains  m  objects described by  n  characteristic\nvariables from the target class to be modeled: \n 7 \n 1 = X b PLS + e \n where  1  is the response vector\n( m  × 1) with all elements equal to one,  b \n PLS  ( n  × 1) contains the\nPLS regression coefficients, and  e  ( m  x 1) is the residual vector. The variables or features in  X  must not be centered; otherwise, all variables could become\northogonal to the constant response vector  1 .\nb \n PLS  ( n  × 1) is computed\nby regression of  1  on  K  primary latent\nvariables (LVs) or components as \n 8 \n T = XW \n \n \n 9 \n 1 = Tq \n \n \n 10 \n b PLS = Wq \n where the columns of  T  ( m  ×  K ) contain the scores of  K  significant orthogonal LVs,  W  ( n  ×  K ) holds the PLS loadings of the  K  LVs, and  q  ( K  × 1)\ndenotes the regression coefficients relating  T  to the\nresponse vector  1 . The prediction of the residual sum\nof squares (PRESS) is obtained by Traditional Cross-Validation (TCV)\nto estimate the optimum number of LVs.\nDistance measures are\nderived from the OCPLS model, two of which\nare the score distance (SD), which represents the position of an object\nin the space spanned by the primary OCPLS components, and the absolute\ncentered residual (ACR), which serves as a measure of the dispersion\nof the projection onto the OCPLS regression coefficient vector. Based\non these metrics, the upper control limit (UCL) is calculated for\nthe ACR and used to plot and identify samples belonging to an alien\nclass. The critic points of standard normal distribution with α\n= 0.05 and F-distribution were used to calculate the number of degrees\nof freedom.\nThe Gaussian Radial Basis Function (GRBF) is commonly\nused to develop\na nonlinear OCPLS model. A transformation is applied and centered\nat the positions of training objects such that the number of GRBF\nequals the number of training samples. All variables must be rescaled\nto a range between 0 and 1 to implement the nonlinear GRBF-OCPLS model.\nThe number of LVs and the kernel width parameter can be estimated\nsimultaneously by analyzing the predicted residuals obtained through\ncross-validation. This cross-validation can be performed using a TCV\napproach or Monte Carlo Cross-Validation (MCCV). \n ,\nPartial robust M-regression (PRM) is an effective and reliable\nrobust PLS model that downweights both orthogonal outliers and leverage\nobjects. This leads to more accurate regression coefficients due to\nimproved confidence levels, resulting in better model precision, especially\nwhen dealing with noisy data. In one-class classifiers, differences\namong regular objects are expected and must be allowed in order to\ncapture the natural variation within the same class. Based on a predefined\ncutoff for the percentage of outliers, PRM is applied using all the\ntraining data. Consequently, the objects assigned the lowest weights\nby PRM are identified as outliers. \n −\nThe values of SD and ACR\nindicate whether an object lies inside\nor outside the modeled class region. According to the values of ACR\nand SD, the object in question can be assigned to one of four groups:\nregular or normal objects (region 1), which exhibit both a small SD\nand a small ACR; good leverage objects (region 2), which have a large\nSD and a small ACR; response outliers (region 3), characterized by\na small SD and a large ACR; and bad leverage objects (region 4), which\npresent a large SD and a large ACR. The ACR quantifies the distance\nof a sample from the OCPLS class model. Consequently, samples characterized\nby a low SD and a high ACR are classified as class outliers. Multivariate\nStatistical Quality Control (MSQC) can be useful for detecting objects\nfalling in regions 2, 3, and 4 as different types of outliers. \n ,\nThe genetic algorithm (GA) is an iterative combinational algorithm\ninspired by Mendelian genetics, where a set of initial random variables\n(chromosomes) undergo processes like selection, crossover combinations,\nand mutations until the fittest set of variables is selected according\nto the minimization of a cost function. \n , \n  This cost\nfunction may vary; for example, it could be the root mean squared\nerror of prediction (RMSEP) in regression models  or the misclassification error for a given classifier in\nclassification models.  The aforementioned\nprocesses are repeated several times during generations until a specific\nset of initial variables that provide the best validation results\nare finally selected. Additionally, the nondeterministic nature of\nthe GA may result in local minima, which could be avoided by running\nthe algorithm several times in search of the best fitness value. Fitness\nherein is defined as the inverse of the cost function.\nIn the\none-class genetic algorithm (OGA), a modification of the validation\nsamples used to find the minimum cost is made so that the model is\ntrained with a single class. For this, two pseudo-classes are created\nin the validation process: positive and negative. The positive class\ncomprises the samples with smaller distances between them and the\nclass center of the target class in a Euclidian space and, thus, the\nsamples with profiles closer to the class mean. The negative class\ncomprises samples with larger distances to the class center, such\nas outliers or borderline samples present in the target class. To\nmake this selection during the GA process, the Kennard–Stone\n(KS) algorithm  is applied to separate\nthe positive and negative classes; the positive being the samples\ncloser together and closer to the class mean, and the negative being\nthe outer samples. After class separation, the cost function used\nto distinguish the classes was based on an LDA classifier defined\nas \n 11 \n G = 1 N v ∑ n = 1 N g n \n where  N \n v  is the\nnumber of validation samples and  g \n \n n \n  is defined as \n 12 \n g n = r 2 ( x n , m I ( n ) ) min I ( m ) ≠ I ( n ) ⁡ r 2 ( x n , m I ( m ) ) \n where  r \n 2 ( x \n \n n \n ,  x \n \n I ( n ) ) is defined as the squared Mahalanobis\ndistance between sample  x \n \n n \n  and the center of the positive class  m \n \n I ( n ) , and  r \n 2 ( x \n \n n \n ,  x \n \n I ( m ) ) is the\nsquared Mahalanobis distance between sample  x \n \n n \n  and the center of the negative class  m \n \n I ( m ) . GA was\nperformed three times starting from different random initial populations,\nand the variables with the best fitness value were selected to build\nthe further OCC models. The GA model was built using 100 generations\nwith 200 chromosomes each. Crossover and mutation probabilities were\nset to 60% and 10%, respectively. The positive class was defined as\nthe 70% of samples closer to the class center of the target class,\nwhile the negative class was defined as the remaining 30% of samples.\nThe OGA schematic workflow is shown in  Figure  \n , where the steps until the selected variables\nare achieved is described.\nOne-class genetic algorithm (OGA) schematic\nworkflow.\nThe performances\nof the DD-SIMCA and OCPLS models were evaluated under identical spectral\npreprocessing conditions, in terms of sensitivity (SEN) of an external\nprediction set, defined as \n 13 \n SEN = number of true positives number of target samples \n where SEN is the ratio between the number\nof true positives and the number of target samples. \n ,\nAll the models were built within the MATLAB R2024b environment\n(MathWorks, Inc., USA) using lab-made routines. Additionally, the\nDD-SIMCA and OCPLS models were built using the DD-SIMCA Toolbox  and OCPLS Toolbox.\nThe COVID-19 samples\nwere made available by the Central Laboratory of Dr. Almino Afonso\n(LACEN), affiliated with the Federal University of Rio Grande do Norte\n(UFRN), Brazil. The samples were collected in public health units\nin the State of Rio Grande do Norte, Brazil, and the patients/volunteers\nread and signed the Free and Informed Consent Form. The study received\nethical approval from the ethics committee under protocol number 65128122.​3.0000.​5537,\nand all procedures were conducted in conformity with the Declaration\nof Helsinki. To carry out the experiments, nasopharyngeal secretion\nwas collected assisted by a nasal swab, fully sterilized, and carefully\nintroduced into the nostril following rotation movements. Before the\nprocedures, the swab was added to a salt solution, which was part\nof the collection kit. These samples were stored at a temperature\nrange between 2 and 8 °C for a maximum of 3 days and stored at\n−80 °C in a freezer. This control-case study resulted\nin a total of 173 samples, with 84 for the healthy control group and\n89 with a clinical diagnosis of COVID-19. All patients were confirmed\nas a control or case using the Reverse Transcription Polymerase Chain\nReaction (RT-PCR).\nNIR spectra were obtained using an ARCoptix\nFT-NIR Rocker spectrophotometer (Arcoptix S.A., Switzerland). The\ntests were carried out in transflectance mode, with a spectral resolution\nof 8 nm. The analytical procedure consisted of transferring 10 μL\nof the sample to an aluminum paper surface and using an optical fiber\npositioned onto each paper. The measurements were repeated 5 times.\nThen, the spectral data were cut in the 1000–2500 nm fingerprint\nand preprocessed with Extended Multiplicative Signal Correction (EMSC,\nfirst order polynomial fitting) and Savitzky–Golay smoothing\n(SG, window of 7 points with first order polynomial fitting was applied),\nwith all parameters fixed.\nThe endometriosis\nsamples were obtained at Januário Cicco Maternity School (MEJC),\naffiliated with the Federal University of Rio Grande do Norte (UFRN),\nBrazil. The study received ethical approval from the ethical committee\nat MEJC/UFRN under protocol no. 44352921.​6.0000.​5292,\nand all procedures were conducted in compliance with the Declaration\nof Helsinki. To conduct the experiments, venous blood samples were\ncollected from each patient and then centrifuged at 3600 rpm for 7\nmin to separate the plasma. 100 μL aliquots of plasma were transferred\nto Eppendorf tubes and stored at −80 °C until the spectroscopic\nanalysis. This control-case study resulted in a total of 75 samples,\nwith 41 samples derived from women with a clinical diagnosis of endometriosis\n(case,  n  = 41) and 34 samples from the healthy control\ngroup ( n  = 34). The analytical procedure for acquiring\nthe NIR spectra of endometriosis was developed as described in ref  . The spectral data were\npreprocessed with MSC and SG smoothing (in MSC, the average spectrum\nwas used, and in SG, a window of 15 points with first order polynomial\nfitting was applied), with all parameters fixed.\nDengue ( n  = 88) vs healthy control ( n  = 90) patients were\nalso investigated using attenuated total reflection Fourier transform\ninfrared (ATR-FTIR) spectra collected from blood samples. This data\nset is derived from Santos et al.  and\npublic available on the Figshare repository,  whose spectroscopic data acquisition is available elsewhere.  The spectroscopic data at the fingerprint region\n(900–1800 cm –1 )  were first analyzed to find possible outliers using the Hotelling’s  T \n 2  vs  Q  residuals test.  Two outliers were identified in the healthy\ncontrols data and removed; thus, the final data set contained 88 dengue\nand 88 healthy control samples. The spectral data were then preprocessed\nby MSC (the average spectrum was used) and SG smoothing (window of\n7 points with first order polynomial fitting was applied), with all\nparameters fixed.\n\nThe preprocessed infrared spectra (MIR/NIR) for the three data sets\napplied in this study are depicted in  Figure  \n . The NIR spectra of the COVID-19 samples\n( Figure  \n a) show the\n−CONH 2  primary amides first and second overtones\nat 1450 and 2016 nm, respectively. The main difference between the\ntwo classes occurs due to the band displacement at 2363 nm, referring\nto the CH stretching and C–C stretching from lipids.\nPreprocessed NIR spectra for (a) COVID-19, (b) endometriosis,\nand\n(c) dengue data sets.\nIn addition, for the NIR spectra of the endometriosis\ndata set\n( Figure  \n b), it is\npossible to observe the −CH 2  second overtone at\n1179 nm, as well as the first overtone of N–H stretching and\nthe first overtone of O–H stretching. The feature at 1788 nm\nis associated with lipid structures. The band at 1950 nm corresponds\nto the second overtone of C–O stretching in carbohydrates,\nwhile the band at 2332 nm is related to the stretching and bending\nof CH associated with methylene. \n , ,\nFurthermore, the ATR-FTIR spectra for the virus\ndata set show four\nmain bands. The first one, at 1641 cm –1 , can be\nassociated with amide I, while the second at 1547 cm –1  is related to the amide II band of proteins. In addition, the bands\nat 1396 and 1454 cm –1  correspond to the symmetric\nCH 3  bending of methyl groups of proteins and asymmetric\nmethyl deformation, respectively. \n , \n  However, for\nthe three examples, it is possible to notice a high similarity between\nboth spectra (case and control), indicating a spectral overlap from\nthe groups when plotted together; thus, it is not possible to distinguish\nbetween them visually. For this reason, it is necessary to use a strategy\ncapable of differentiating between the samples. In this context, the\none-class classifier models are a powerful tool to identify samples\nof clinical interest (case group), since these models help to detach\nthe target sample from all the other classes,  especially when combined with variable selection methods, such as\nthe OGA, developed in this study.\nThe one-class classifier\nmodels were developed using Linear OCPLS, GRBF-OCPLS, PRM-OCPLS, and\nDD-SIMCA. The performance of these models for the COVID-19, endometriosis,\nand dengue data sets, both before and after variable selection using\nOGA, was evaluated using a rigorous approach.  This strategy was defined with a significance level of α =\n0.05, and the results for the quality parameters are presented in  Table  \n .  The SEN value denotes the percentage of target class samples\nthat are correctly classified as belonging to the target class.\nSEN TRAIN, sensitivity of training.\nSEN PRED., sensitivity of prediction.\nThe acceptance plots of\nthe one-class models for the COVID-19 data are presented in  Figure  \n . Outliers detected\nin the samples were removed prior to the application of the DD-SIMCA\nmodel for each preprocessed data set. The first row ( Figure  \n a,b) of acceptance plots corresponds\nto the models built with the entire NIR spectrum and shows a good\nperformance for classifying the COVID-19 samples by using 3 PCs, while\nthe models built with variable selection (shown in the second row,  Figure  \n c,d) present a better\nresult when using 4 PCs.\nAcceptance plots of the DD-SIMCA models for\nthe COVID-19 data.\nThe first row shows the results without variable selection: (a) acceptance\nplots of the COVID-19 calibration data set and (b) COVID-19 and control\ntest data set. This model was built using 3 PCs. The second row shows\nthe results with variable selection: (c) acceptance plots of the COVID-19\ncalibration data set and (d) COVID-19 and control test data set. This\nmodel was built using 4 PCs. All models were built using the confidence\nlevel of 95% (α = 0.05).\nThus, when comparing the last acceptance plot in\neach row (the\ncontrol data set), it can be seen that variable selection improves\nboth the sensitivity and the selectivity for the training and test\nof target samples (COVID-19) and the new control test data sets. Specifically,\nthe application of variable selection resulted in a greater number\nof correctly classified samples. This indicates an improved model\ncapacity to correctly classify the control class when using the OGA\nvariable selection method since this variable selection algorithm\naims to extract useful information from large and complex data sets,\nsuch as the IR spectra, which can carry most of the important information\nfrom the samples with minimal noise, improving the classification\ncapacity of the model.\nThe acceptance\nplots for the endometriosis spectra are shown in  Figure  \n . Similarly to the\nCOVID-19 samples, outliers were removed prior building the DD-SIMCA\nmodels for each preprocessed data set. The acceptance plots are shown\nin  Figure  \n . The model\nwithout variable selection used 2 PCs, while the model using the OGA\nused 3 PCs.\nAcceptance plots of the DD-SIMCA models for the endometriosis data.\nThe first row shows the results without variable selection: (a) acceptance\nplots of the endometriosis calibration data set and (b) endometriosis\nand control test data set. This model was built using 2 PCs. The second\nrow shows the results with variable selection: (c) acceptance plots\nof the endometriosis calibration data set and (d) endometriosis and\ncontrol test data set. This model was built using 3 PCs. All models\nwere built using the confidence level of 95% (α = 0.05).\nComparing the last acceptance plot in each row,\nit is observed\nthat variable selection improves both the sensitivity and selectivity\nlevels for the training and test of the endometriosis class and the\nnew control test data sets. The model’s ability to correctly\nclassify the control class remains essentially unchanged when applying\nthe variable selection.\nFinally, the acceptance plots for the\ndengue data are presented\nin  Figure  \n . As in\nthe other applications, the outliers were removed prior to building\nthe DD-SIMCA models for each preprocessed data set in order to improve\nthe classification performance of this model. \n , \n  For this data set, both models were built by using only 1 PC.\nAcceptance\nplots of the DD-SIMCA models for the dengue data. The\nfirst row shows the results without variable selection: (a) acceptance\nplots of the control calibration data set and (b) control and dengue\ntest data set. This model was built using 1 PC. The second row shows\nthe results with variable selection: (c) acceptance plots of the control\ncalibration data set and (d) control and dengue test data set. This\nmodel was built using 1 PC. All models were built using the confidence\nlevel of 95% (α = 0.05).\nFurthermore, when comparing the last acceptance\nplot in each row,\nit is observed that variable selection improves both selectivity levels\nfor the training and test of the control and the new dengue test data\nsets. The application of variable selection resulted in a greater\nnumber of correctly classified samples. This indicates an improved\nmodel capacity to correctly classify the dengue class when the OGA\nvariable selection is used.\nAlthough the DD-SIMCA sensitivity\nfor COVID-19 improved following\nthe application of OGA, the performance remains suboptimal, as only\na modest enhancement in sample-classification accuracy was observed.\nThe high sensitivity reflects that all of the COVID-19 samples were\ncorrectly identified; however, the model still produced misclassifications\nby erroneously assigning samples from other classes to the COVID-19\nclass. This same trend is also observed to a minor degree for endometriosis\nand could be caused by the DD-SIMCA classification threshold that\nprioritizes nonfalse negative classification in detriment of possible\nfalse positives. In addition, limitations associated with the spectral\ninformation for this data set based on NIR spectroscopy may contribute\nto the poor classification of negative samples, as NIR data have more\nnoise and band overlapping than FTIR, for example. Thus, the inherent\ncomplexity of NIR observed in the COVID-19 and endometriosis data\nsets may be difficult to classify when compared to dengue (obtained\nby FTIR).\nIn addition to the DD-SIMCA\nmodels, OCPLS models were also built for the three data sets studied.\nThis model was applied in three ways, which are the ordinary OCPLS,\nthe nonlinear Gaussian Radial Basis Function (RBF or GRBF)-OCPLS,\nand the OCPLS based on partial robust M-regression (PRM). However,\nas depicted in  Table  \n , the best classification performance was obtained by the PRM-OCPLS\nfor the three IR data sets. This model probably had a better classification\nperformance since it can detect the orthogonal and leverage outliers\nand then be used to develop an ordinary OCPLS model without the presence\nof outliers, differently from DD-SIMCA, for example. \n ,\nFigure  \n  shows\nthe plots for the PRM-OCPLS models with the COVID-19 data. As in the\nDD-SIMCA approach, the robust PRM models were built after removing\noutliers. In the first row ( Figure  \n a–c), the model was built using the training\nset without variable selection and with 5 LVs. For the second row\n( Figure  \n d–f),\nthe model was built using the training set with variable selection\nand with 7 LVs. Comparing the last plot of the first row with that\nfrom the second row, a slight improvement in the correct classification\nsamples is observed. This slight improvement indicates that the model’s\nability to correctly classify the control class remains essentially\nunchanged when applying the OGA, with the number of samples in region\n1 (regular region) practically remaining the same.\nPlots of the PRM-OCPLS models based on the NIR preprocessed spectral\ndata for COVID-19. The first row shows the results without variable\nselection: (a) standard deviation of residuals obtained for each LV\nusing Traditional Cross-Validation (TCV), (b) ACR and score distances\nfor the training data set using PRM-OCPLS with 5 LVs, and (c) ACR\nand score distances for the test set containing new COVID-19 samples\nand control data set. This model was built using 5 LVs. The second\nrow shows the results with variable selection: (d) standard deviation\nof residuals obtained for each LV using Traditional Cross-Validation\n(TCV), (e) ACR and score distances for the training data set using\nPRM-OCPLS with 7 LVs, and (f) ACR and score distances for the test\nset containing new COVID-19 samples and control data set. This model\nwas built using 7 LVs. All models were built using the confidence\nlevel of 95% (α = 0.05).\nFigure  \n  shows the\nplots for the PRM-OCPLS models with the endometriosis data. The robust\nPRM models were built after removing outliers. In the first row, the\nmodel was constructed using the training set without variable selection\nand with 5 LVs, while in the second row, the model was built using\nthe training set with variable selection and 6 LVs. Comparing the\nlast plots of both rows ( Figure  \n c,f), in both cases, without and with variable selection,\nthe models were able to achieve complete separation of the control\ntest class from the modeled target class.\nPlots of the PRM-OCPLS\nmodels based on the NIR preprocessed spectral\ndata for endometriosis. The first row shows the results without variable\nselection: (a) standard deviation of residuals obtained for each LV\nusing Traditional Cross-Validation (TCV), (b) ACR and score distances\nfor the training data set using PRM-OCPLS with 5 LVs, and (c) ACR\nand score distances for the test set containing new endometriosis\nsamples and control data set. This model was built using 5 LVs. The\nsecond row shows the results with variable selection: (d) standard\ndeviation of residuals obtained for each LV using Traditional Cross-Validation\n(TCV), (e) ACR and score distances for the training data set using\nPRM-OCPLS with 6 LVs, and (f) ACR and score distances for the test\nset containing new endometriosis samples and control data set. This\nmodel was built using 6 LVs. All models were built using the confidence\nlevel of 95% (α = 0.05).\nFigure  \n  shows the\nplots for the PRM-OCPLS models of dengue data. The robust PRM models\nwere built after removing outliers. In the first row, the model was\nconstructed using the training set with the full spectra and with\n6 LVs, while in the second row, the model was built using the training\nset with the variable selected by the OGA and 5 LVs. Comparing the\nlast plots of both rows ( Figure  \n c,f), it is observed that this large increase in correctly\nclassified samples indicates that the selected variables effectively\ndiscriminated dengue samples from region 1 (regular region) to region\n3 (class outlier), which resulted in a better model. This better model\nintrinsically brings improvements provided by variable selection probably\ndue to the extraction of important features from the data. \n ,\nPlots\nof the PRM-OCPLS models based on the FTIR preprocessed spectral\ndata for dengue. The first row shows the results without variable\nselection: (a) standard deviation of residuals obtained for each LV\nusing Traditional Cross-Validation (TCV), (b) ACR and score distances\nfor the training data set using PRM-OCPLS with 6 LVs, and (c) ACR\nand score distances for the test set containing new control samples\nand dengue data set. This model was built using 6 LVs. The second\nrow shows the results with variable selection: (d) standard deviation\nof residuals obtained for each LV using Traditional Cross-Validation\n(TCV), (e) ACR and score distances for the training data set using\nPRM-OCPLS with 5 LVs, and (f) ACR and score distances for the test\nset containing new control samples and dengue data set. This model\nwas built using 5 LVs. All models were built using the confidence\nlevel of 95% (α = 0.05).\nThe\napplication of the OGA in this study is a way for improving the performance\nof the OCC models, as can be seen in  Table  \n . This happens since the variable selection\nalgorithms can identify informative variables out of the full IR spectra,\nand with the removal of the irrelevant information within the system,\na much simpler and parsimonious model can be obtained, without compromising\nits predictive ability. \n , \n  The variables selected\nby the OGA for the three data sets are depicted in  Figure  \n .\nSelected variables responsible\nfor class separation by the OGA:\n(a) COVID-19, (b) endometriosis, and (c) dengue.\nThe OGA selected 32 wavelengths that were responsible\nfor the correct\nclassification of the COVID-19 samples. The tentative biomarker assignments\nfor these selected variables are shown in  Table  \n . Is it possible to highlight bands at 2499,\n1925, 1498, and 1387 nm, which correspond to the C–H stretching\nand C–C and C–O–C stretching combination band\nof polysaccharides, −CONH– second overtone of secondary\namides, −CONH 2  first overtone of primary amides,\nand the C–H stretching and CH deformation from carbohydrates,\nrespectively. These bands can be identified as potential classifier\nbiomarkers since they correspond to some biological molecules that\ncan be significantly altered in patients with COVID-19 due to a series\nof metabolic alterations in the human body by the SARS-CoV-2 virus. \n −\nWhen applying the algorithm to the endometriosis data\nset, the\nOGA selected 15 wavelengths that were responsible for the correct\nclassification of the endometriosis samples. The tentative biomarker\nassignments for these selected variables are shown in  Table  \n . The band selected at 2371\nnm corresponds to CH stretching and C–C stretching combination\nfrom lipids, and the band at 1990 nm can be associated with the combination\nband of NH stretching + amide. The bands at 1612 and 1095 nm are\nrelated to the first overtone of the intermolecular hydrogen bond\nfrom primary amines and the second overtone of the hydrogen bond for\nsecondary amides, respectively. These variables are in accordance\nwith previous results obtained by the GA for discriminant analysis.\nFinally, 31 wavenumbers were selected with the OGA\nfor the dengue\ndata set, which were responsible for the correct classification of\nthe virus samples. The tentative biomarker assignments for these selected\nvariables are listed in  Table  \n . By analyzing the selected wavenumbers, it is possible to\nconclude that OGA attributed the main variables for one-class classification\nbetween the classes to phosphodiester groups of nucleic acids (phosphate\nI in RNA) at ∼1078 cm –1 ; amide I (∼1668\ncm –1 ); and amide II (∼1552 cm –1 ), which are in accordance with previous studies involving variable\nselection for virus discrimination.\n\nIn this study, one-class\nclassifier models associated with a new\nvariable selection strategy, the one-class genetic algorithm (OGA),\nwere applied to clinical data. Although both models provided similar\nclassification results, for the COVID-19 data, the OGA-PRM-OCPLS showed\nmore robust classification than DD-SIMCA. The same happened for the\nendometriosis and dengue data. Furthermore, the wavelength and wavenumbers\nselected in the three data sets studied could be related to biomarkers\ncapable of differentiating the classes, providing valuable biochemical\ninformation for the detection of COVID-19, endometriosis, and dengue.\nHerein, for the first time, the OGA associated with the OCC models\nis reported, such as DD-SIMCA and OCPLS, and they can be implemented\nas screening models in clinical applications using spectroscopy, highlighting\ntheir potential for less expensive and less time-consuming analyses.\nHowever, some limitations including the small sample size, need for\nindependent data set validation, and nondeterministic nature of the\nOGA must be taken into account before considering this approach for\ngeneralizability and clinical implementation.","source_license":"CC-BY-4.0","license_restricted":false}