# A Comparison of PCA-LDA and PLS-DA Techniques for Classification of Vibrational Spectra
## 3 Results and Discussion
Loading 4 spectrum is reported in (**b**). The positive peaks in Figure 5b correspond to Raman peaks due to nucleic acid cellular components, while the spectral positions of the negative peaks correspond to spectral Raman signals related to cellular protein and lipid components, as discussed above. Finally, PCA results for the dataset of MCF7 and MDA cells are shown in Figure 6. For the FTIR spectra of this dataset, the first 7 principal components carried around 97% of all the spectral variation found in the whole dataset. The score plot in Figure 6a highlights that PC1 well discriminate the metastatic MDA cells from the malignant MCF7 ones, with almost no overlapping score values. In particular, MCF7 and MDA cells have positive and negative, respectively, PC1 score values and the box plots at the top of Figure 6a demonstrates that the two distribution are statistically different, according to \(t\)-test analysis. Furthermore, the loading 1 plot in Figure 6b is very similar to the difference plot in Figure 3c, indicating that MCF7 cells (positive score) have a large relative content of nucleic acid components (positive loading bands at about 1085 and 1230 cm\({}^{-1}\)) with respect to MDA  
Figure 5: PC4 vs. PC1 score plot (**a**) for the control (blue dots) and exposed (red dots) Raman spectra of MCF10A cells. The box plots of the PC4 score values are shown on the right side of (**a**): the results of the \(t\)-test point out that the two distributions of score values are significantly different (\(p=0.001\)). Loading 4 spectrum is reported in (**b**). cells, whereas the spectral features in the 1500-1700 cm\({}^{-1}\) range are related to the shift of the spectral position of amide I and II bands for the two types of cell. Overall, the presence of several peaks in the loading plots of the discriminating PCs and the agreement of their spectral positions with those of the difference plots confirmed the discrimination potential of vibrational spectra. Therefore, classification techniques can be applied to the test sets of the three datasets, in order to evaluate the discrimination performance. Hence, following the PCA, linear discrimination analysis was first performed. The first seven PC scores of the calibration set of simulated spectra were used as input data for LDA to build a diagnostic model that will be used for the classification of unknown spectra. The PCA-LDA model correctly classifies all the 36 spectra, as visible in the classification  
Figure 6: PC2 vs. PC1 score plot (**a**) for the MCF7 (blue dots) and MDA (red dots) FTIR spectra. The box plots of the PC1 score values are shown at the top of (**a**): the results of the \(t\)-test point out that the two distributions of score values are significantly different (\(p<0.001\)). Loading 1 spectrum is reported in (**b**). plot shown in Figure 7a (filled circles). In fact, a discriminant score for the attribution of an object (spectrum) to each class is calculated and the object is assigned to that class for which the discriminant score is the largest. Hence, in Figure 7a samples lying close to zero for a class are associated with that class. Instead, the accuracy of the PCA-LDA model for the classification of Raman spectra from unexposed and proton-exposed MCF10A cells, shown in Figure 7b is 87.5%. Indeed, such a model, obtained by using the first seven PC scores of the calibration set as input for the LDA model, erroneously attributes some samples of the calibration set to a different class from the one they actually belong to, as visible in Figure 7b from the circle crossed samples. In particular, 4 control spectra were attributed to exposed class and 1 exposed spectrum was attributed to control class. Lastly, a 100% accuracy is obtained for the PCA-LDA classification model related to MCF7 and MDA cells, as visible in Figure 7c. Figure 7: Discrimination plot obtained from the results of Linear Discriminant Analysis model developed using 7 principal components from Principal Component Analysis.