# A Comparison of PCA-LDA and PLS-DA Techniques for Classification of Vibrational Spectra
## 3 Results and Discussion
The spectral differences between mean values are reported in (**c**) and the wavenumber values of spectral features mainly contributing to such a difference are labelled for clarity. The difference plots indicate that, for all three cases, important intensity differences between the mean spectra of two types of cells characterize the investigated range. In order to show whether these spectral differences would be enough to discriminate and classify the two types of cells, we firstly analysed data by means of the PCA technique. In particular, samples from the calibration sets were analysed by PCA, using a full cross-validation method. Although PCA is not able to provide classification, it is largely used for data interpretation and visualization, as well as to reduce dimension by extracting information from high-dimension data to project them into a lower dimension. In particular, PCA score plots are able to visualize the similarity and differences between samples and PCA loading plots provide information about the spectral variables responsible for the differences. Figure 4a shows the score plots of PC1/PC4, with the percentage of each PC in the axis, for the simulated dataset. It has been verified that the first 7 principal components carried around 99% of all the spectral variation found in the dataset. As is visible in the score plot, the PC4 provides the main contribution to the discrimination of control-like spectra from exposed-like ones. In particular, control-like spectra have negative PC4 values and exposed-like spectra are characterized by positive PC4 values, with minor overlap. The results of the \(t\)-test analysis performed for the distributions of PC4 score values for the two types of spectra prove that they are significantly different, as deduced from the box plots on the right side of Figure 4a. The representation of the loadings of PC4 in Figure 4b points out four intense negative peaks (at 785, 830, 1090 and 1580 cm\({}^{-1}\)) whose spectral positions correspond to those of the four positive peaks in the difference of mean  
Figure 3: FTIR spectra of MCF7 (**a**) and MDA (**b**) cells. The mean spectra are reported by blue and red lines in (**a**,**b**), respectively. Standard deviation spectra are also reported as dashed lines and the grey area corresponds to spectral values between mean \(\pm\) standard deviation values. The spectral differences between mean values are reported in (**c**) and the wavenumber values of spectral features mainly contributing to such a difference are labelled for clarity. spectra shown in Figure 1c. Therefore, PCA confirms that the two types of spectra can be mainly discriminated according to PC4 and such discrimination is related to the simulated spectral peaks whose intensity was changed to differentiate between control-like and exposed-like spectra. Similar results occur for Raman spectra of control- and proton-exposed MCF10A cells. For the spectra of such cells, the first 7 principal components carried around 90% of all the spectral variation found in the whole dataset. The score plot in Figure 5a points out that the PC4 component discriminates control from exposed cells, where control cells present mainly positive PC4 score values and exposed cells have mainly negative PC4 score values. Although overlapping score values are more major than in Figure 4a, the distributions of score values are statistically different, as can be deduced from the box plots on the right side of Figure 5a obtained by the \(t\)-test analysis. A confirmation that PC4 discriminates between the two types of cells is obtained from Figure 5b, where values of PC4 loadings are shown. The similarity of the spectrum in Figure 5b with that in Figure 2c is very evident. Figure 4: PC4 vs. PC1 score plot (**a**) for the synthetic control (blue dots) and exposed (red dots) vibrational spectra. 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 (\(p<0.001\)).