## 3 Results and Discussion
The classification model that we used, known as PCA-LDA, firstly uses linear combinations of some PCA scores of the calibration set to build and optimize a model that maximizes the separability between classes. In this stage, the model works in a supervised way, that is, it is provided with the classes to which each Raman spectrum belongs. Then, the spectra of the test set are provided to the developed and optimized model, without specifying the class to which they belong, in order to evaluate the attribution that the model outputs. Taking into account the PCA results, the scores of the first 10 PCs and 6 PCs of the Raman spectra from the calibration set were used as input parameters to develop an LDA model for the nucleus spectra and cytoplasm spectra, respectively. The constructed PCA-LDA model is shown by filled circles in Figure 3a,b for the nucleus spectra and cytoplasm spectra, respectively. Since the model is developed by assigning to each spectrum a  
Figure 2: PC2 vs. PC1 (**a**) and PC3 vs. PC2 (**b**) score plot for the Raman spectra of the calibration set. Difference in mean spectra (cancer–healthy signal) and loading 2 and loading 3 spectra are also reported for the Raman nucleus spectra (**c**) and Raman cytoplasm spectra (**d**). discriminant score value for belonging to each of the two classes and each spectrum is assigned to the class for which this value is larger [26], it is evident in Figure 3 that each spectrum is correctly classified during the model building stage. Indeed, the discriminant score value is negative, and the closer it is to zero, the greater the value. The test set spectra have been used to estimate the classification accuracy of the constructed PCA-LDA model. The projection of the test set spectra onto the PCA-LDA plot in Figure 3 (hollow circles) highlights that the discriminant score values of the test set spectra correctly classify them (this can be inferred from the higher discriminant score value for belonging to the right class). Therefore, an excellent (100%) classification accuracy has been obtained for both nucleus spectra and cytoplasm spectra by means of the constructed PCA-LDA model. Recently, there has been widespread use of the PCA-LDA technique for classifying Raman spectra measured on healthy and colon cancer biological samples, although there is a lack of recent research on colon cells. In particular, colon cancer diagnostic investigations by means PCA-LDA of surface-enhanced Raman spectroscopy (SERS) of human serum reported accuracy values of 87.5% [27] and 84.1% [28]. Moreover, a PCA-LDA-based investigation of Raman spectra measured for human colorectal tissue samples stated sensitivity and specificity values of 82% and 51%, respectively [29]. The above works used a cross-validation strategy to estimate the classification parameters. The difference between our investigation and that of the above authors consists in the validation stage of the constructed PCA-LDA model. In particular, we separated the model building stage (for which we used calibration set spectra) from the classification accuracy estimation stage (which we performed by using test set spectra). In fact, we have used a full cross-validation only during the model building stage, in order to optimize the number of PCs to be used. The estimation of classification accuracy using an independent set of spectra (test set) is considered to provide a more realistic estimate of the classification performance [26]. In addition, [PERSON] et al. performed SERS measurements of human serum of healthy people and colon cancer patients: such spectra, combined with a PCA-LDA model, detected colon cancer with 90% accuracy [30]. However, they stated that the serum spectral dataset was used to train the classification algorithm, but they did not mention any validation stage of the constructed model. Besides the PCA technique, the PLS method is also frequently used to reduce and model spectral data.