# A Comparison of PCA-LDA and PLS-DA Techniques for Classification of Vibrational Spectra
## 3 Results and Discussion
The scatter plot shows the discrimination of synthetic control-like spectra (filled blue circles) and exposed-like vibrational spectra (filled red circles) in (**a**), that of Raman spectra of control (filled blue circles) and exposed (filled red circles) MCF10A cells in (**b**) and that of FTIR spectra of MCF7 (filled blue circles) and MDA (filled red circles) cells in (**c**). Crossed circles in (**b**) are related to samples of the calibration set which are erroneously attributed to the PCA-LDA model. The projections of the test samples on the PCA-LDA model are shown as hollow circles. One misclassified sample of the test set is enclosed inside a circle and labelled in (**b**). Despite the small number of spectra used by us, the accuracy value of the PCA-LDA model is similar to that obtained by [PERSON] et al. regarding the discrimination of two different types of breast cancer tissue from healthy breast tissue by means of Raman spectroscopy: in fact, their accuracy, validated through full cross-validation, is equal to 88.3% [34]. Furthermore, [PERSON] et al. declared to discriminate breast cancer by SERS spectra of serum proteins from cancer patients with respect to those from healthy volunteers with the PCA-LDA model, achieving an accuracy value of 84% with a ten-fold cross-validation method [35]. Similar accuracy values with the PCA-LDA algorithm applied to Raman spectra have been obtained for discrimination of normal parenchyma and follicular patterned thyroid nodules (78%) and for carcinoma versus adenoma follicular lesions (89%) [36]. Furthermore, Raman spectra from normal and tumour oral tissues were differentiated under the PCA-LDA model with an accuracy of 81.25% with full and k-fold cross-validation methods [37]. Instead of cross-validation, we prefer to estimate the sensitivity and specificity of the classification model using a set of data (test set) that are external and independent of those used to build the model. This procedure is performed in view of its possible use in a clinical setting for diagnostic purposes. Indeed, in this case, some spectra should be acquired from areas containing material (cells, tissues) that are difficult to diagnose and the classification technique applied to these spectra, having available a dataset of spectra previously acquired from pathological and healthy areas. Therefore, the prediction parameters of the developed PCA-LDA model were tested using samples of the test sets from the two classes. The results of the model prediction are summarized in Table 1. Almost all the tested samples were predicted as belonging to the proper class, except one MCF10A exposed sample which is attributed to the control class. Therefore, the model was able to rightly classify the test samples and the accuracy, sensitivity and specificity achieved maximum values in the cases of simulated spectra and FTIR spectra, whereas these values were 93%, 86% and 100%, respectively, in the case of proton-exposed MCF10A cells. In order to obtain a visual picture of the classification performance, the test samples were projected on the classification plot in Figure 7, where they are represented by hollow circles. It is clearly visible that all the representative points of the test set samples are in proximity to the representative points of the calibration set samples, with only one exception in Figure 7b due to an MCF10A exposed sample which has been misclassified, as discussed above. The procedure of optimizing the model using a calibration test with cross-validation and then evaluating the model performance using a test set was also carried out by [PERSON] et al., who measured Raman spectra from various types of breast cancer [38]. In particular, they found that the PCA-LDA model correctly classifies all samples in the test set. Furthermore, [PERSON] et al.