# A Comparison of PCA-LDA and PLS-DA Techniques for Classification of Vibrational Spectra
###### Abstract
showed that Raman spectroscopy can identify changes in the molecular composition of healthy astrocytes compared to glioblastoma patient-derived cells and that, associated with PCA-LDA, can become a diagnostic tool with accuracy values between 80% and 100% [18]. PCA-LDA statistics were also used to classify oral squamous cell carcinoma cells in saliva samples with an accuracy of 90%, in the case of the Raman data set, and 82%, for the FT-IR one [19]. The PCA-LDA model also has been demonstrated to yield 100% classification accuracy to differentiate FTIR spectra from hepatitis C infected and healthy freeze-dried sera samples [20]. The PCA-LDA discrimination model correctly classified also FTIR spectra from gynaecological cancer samples into malignant and benign groups with accuracies of 96% and 93% for the k-fold and \"leave one out\" validation schemes, respectively [21]. PLS-DA is a supervised classification technique which combines partial least squares (PLS) regression with LDA. Firstly, a PLS model is built from the spectral data (X matrix) and a dependent variable describing the class of spectra (Y matrix), so that Y = XB + E, where B is a matrix of regression coefficients and E is a matrix of residuals. The X matrix consists of \(n\) rows, each one related to a sample, and \(m\) columns, each one related to the signal intensity for each wavenumber value, whereas the Y matrix consists of \(n\) rows, each one is a categorical variable that specifies the type of sample (samples of different type are described by different discrete numbers that encode the class membership, as \(-1\) and \(+1\)). Such a PLS model, that relates the variations of the spectral data to the class of cells from which the spectra were measured, firstly transforms the original spectral variables into a set of a few latent variables (LVs), called factors. Then these new variables are used for regression with the dependent variable [11,22]. In the PLS models, scores and loadings specify how the samples and variables are projected along the factors. In particular, PLS scores, similarly to PCA scores, are the sample coordinates along the model components: they are computed in such a way that they capture the part of the structure in X which is most predictive for Y. The PLS loadings specify how much each X-variable contributes to a specific model component, in the same way as the PCA loadings do. A two-dimensional scatter plot of scores for two specified factors gives information about patterns in the samples, i.e., the closer the samples are in the scores plot, the more similar they are with respect to the two components concerned, whereas distant samples in the score plot are different. The corresponding loadings plot provides information about which variables are responsible for differences between samples. In addition, the regression coefficients determine what is the weight of each variable when predicting a particular Y response, i.e., variables with a large regression coefficient play an important role in the regression model. A positive coefficient shows a positive link with the response, and a negative coefficient shows a negative link. The difference between loadings and regression coefficients is that the former is related to each LV, whereas the latter refers to a model with a specific number of LVs. After the PLS regression model has been built, a linear discriminant classifier is used for classifying unknown samples (spectra). When \(-1\) and \(+1\) are the encoded values of class membership, if the predicted value is above 0, a corresponding object is considered a member of a class and if not it is considered a stranger. Recently, PLS regression algorithms have been widely used in the biomedical field to construct predictive models based on Raman and FTIR spectral signals. [PERSON] et al. classified Raman spectra from brain tissue using PLS-DA discrimination into normal (cerebellum and meninges) and tumours (glioblastoma, medulloblastoma, schwannoma, meningioma) with an accuracy of 94.1% [23].