## 3 Results and Discussion
It differs from PCA because both the spectral data and the related class membership (coded with numbers) are used together iteratively to build a model. This model is built by linking spectral datasets to numbers encoding class membership  
Figure 3: Discrimination plot built from Raman nucleus spectra (**a**) and cytoplasm spectra (**b**) of the calibration set (filled circles) and projections of the spectra from the test set using the PCA-LDA model (hollow circles). with the aim of optimizing separation between samples belonging to different classes. The PLS model transforms the variables of the original spectral dataset into a set of a few latent variables, called factors, which are computed maximizing the covariance between the original spectral dataset and the numbers encoding class membership [26; 31]. Then, the spectra of the original dataset can be projected onto the subspace of the factors. This projection corresponds to a number predicting the class membership: for example, if +1 and \(-1\) are the encoding values for two classes, a projection value above zero corresponds to membership attributed to the first class, whereas a projection value below zero corresponds to the attribution to the second class. PLS model is characterized by scores and loadings, similarly to PCA. PLS scores are the coordinates of the original spectra along the factors, and they are calculated in such a way that they capture the part of the structure in the original dataset which is most predictive for class membership. The PLS loadings specify how much each original variable contributes to a specific PLS factor. Similar to the PCA-LDA technique, after the PLS model has been built, it can be used with a linear discriminant classifier for classifying unknown spectra. Therefore, we used the calibration set spectra to build a PLS model in order to classify Raman spectra of the test set. Figure 4a,b show the score plots of the nucleus spectra and cytoplasm spectra, respectively, after a full cross-validation procedure. It is clearly evident that in both cases the healthy and cancer spectra are discriminated according to factor 1 values, which are mainly positive for the spectra of healthy cells and negative for the spectra of cancer cells. The first four PLS factors included more than 50% of all the variance of the spectra from calibration set in both calibration sets. The loading 1 plots, shown in Figure 4c,d for the spectra measured inside the two cellular compartments, are quite similar to the difference spectrum (with positive and negative peaks exchanged). Therefore, the PLS model confirms the results obtained by PCA about the main cellular components responsible for the differentiation between healthy and cancer cells. Figure 4: PLS score plot for the Raman spectra of healthy cells and cancerous cells of the calibration set in the nucleus region (**a**) and cytoplasm region (**b**). The corresponding loading 1 and difference of mean spectra are displayed in (**c,d**). Figure 5a,c show the predicted class for the calibration set spectra measured on nucleus and cytoplasm region, respectively. Membership of the healthy and cancer classes has been encoded with \(+1\) and \(-1\) values, respectively. It turns out that all spectra take values close to the reference values. Figure 5b,d show the classification predictions of the PLS model estimated from the test set spectra of the nucleus and cytoplasm region, respectively. Most of the spectra in the test set are correctly encoded and assigned to the proper class. However, the uncertainty bars cross zero in two cases (circled by red ellipses) in both Figure 5b,d. Therefore, a prediction accuracy of the PLS-DA model of 96% for spectra of both nucleus and cytoplasm regions can be estimated. [PERSON] et al. reported that Raman spectra, performed in vivo for colon tissues, were able to separate cancerous tissue from normal tissues with 88.8% accuracy by PLS-DA analysis with leave-one-patient-out cross validation [32]. In a work apparently very similar to ours, [PERSON] et al.