# A Comparison of PCA-LDA and PLS-DA Techniques for Classification of Vibrational Spectra
## 3 Results and Discussion
have recently used Raman spectroscopy and PCA-LDA model for the classification of glioblastoma multiforme cells derived from brain tumour patients versus astrocytes derived from healthy patients, using a test set consisting of different cells than the calibration set [18]. They stated an average classification accuracy of 92.5%. Therefore, the results we obtained about the performance parameters of the PCA-LDA technique applied to different types of vibrational spectra are in good agreement with those reported by other authors about spectra obtained with the Raman technique. Furthermore, a PLS model was built for the calibration set of simulated spectra by using 7 latent variables. Clear discrimination of the control and exposed spectra is visible in Figure 8a, which shows (filled circles) the score plot of Factor 1 and Factor 2 of the PLS model. In particular, the separation between the two types of spectra can be observed along both factors. Such a feature is also confirmed by the plot of the regression coefficients, shown in Figure 8b for two components of the regression model. It can be deduced that the most important variables in the PLS model were those corresponding to wavenumbers around 780, 830, 1090 and 1580 cm\({}^{-1}\), as expected because the spectral peaks centred at such wavenumber values are mainly responsible for the difference between the average spectra of control-like and exposed-like spectra reported in Figure 1c. The performance of the prediction ability of the built PLS model, checked by using just the samples from the test set, is summarized in Table 1. All the unknown samples were correctly assigned to the proper class, so producing maximum values of the performance parameters. Such results can be also visualized by reporting the projections of the test samples on the Factor 2 vs. Factor 1 score plot, shown as hollow circles in Figure 8a. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Simulated Spectra**} & \multicolumn{4}{c}{**MCF10A Cells Raman Spectra**} & \multicolumn{4}{c}{**MCF7 and MDA Cells FTIR Spectra**} \\ \hline
\begin{tabular}{c} Specificity \\ 100\% \\ \end{tabular} \\ \hline
**PLS-DA** & total & \begin{tabular}{c} predicted \\ control- \\ like \\ \end{tabular} & \begin{tabular}{c} predicted \\ exposed- \\ like \\ \end{tabular} & total & \begin{tabular}{c} predicted \\ control \\ \end{tabular} & \begin{tabular}{c} predicted \\ exposed \\ \end{tabular} & total & \begin{tabular}{c} predicted \\ MCF7 \\ \end{tabular} & \begin{tabular}{c} predicted \\ MCDA \\ \end{tabular} \\ \hline actual & 7 & 7 & 0 & 7 & 7 & 0 & \
\begin{tabular}{c} actual \\ MCF7 \\ \end{tabular} & 10 & 9 & 1 \\ \hline actual & 7 & 0 & 7 & 7 & 1 & 6 &
\begin{tabular}{c} actual \\ MDA \\ \end{tabular} & 10 & 0 & 10 \\ \hline total & 14 & 7 & 7 & 14 & 8 & 6 & total & 20 & 9 & 11 \\ \hline \end{tabular}
\end{table} 
Table 1: Performance parameters for the three types of spectra. The parameter values are estimated by considering the results obtained for the spectra of the test sets. Accuracy represents the total rate of spectra correctly classified; sensitivity is the rate of spectra classified as exposed-like (for simulated spectra), exposed (for Raman spectra) and metastatic MDA (for FTIR spectra) with respect to the spectra which refer actually to exposed-like, exposed and MDA samples, respectively; specificity is the rate of spectra classified as control-like (for simulated spectra), control (for Raman spectra) and non-metastatic MCF7 (for FTIR spectra) with respect to the spectra which refer actually to control-like, control and MCF7 samples, respectively. Similarly, the PLS model built for calibration samples of the MCF10A cells clearly discriminates control from exposed cells mainly according to Factor 1, as visible in Figure 9a with the filled circles.