## 3 Results and Discussion
DL models like MLPC can be particularly sensitive to this phenomenon, especially if built with a relatively small-sized dataset, as in this case. The origin of this weakness can be attributed to the high number of parameters that need to be optimized. However, the small errors associated with \(A\), \(S\), and \(SP\) observed in our case are representative of negligible overfitting. As expected, the simplest binary classification problem EC-CS led to the best performance, i.e., \(A=(99.7\pm 0.1)\%\), \(S=(99.7\pm 0.1)\%\), and \(SP=(99.0\pm 0.1)\%\), reached with MLPC(ADAM). This result is in line with previous works about the Raman-based detection of CS and EC [6, 22, 23]. On the other hand, the classification problem EC-G1-G2-G3 resulted in the minimum classification accuracy, with the maximum value of \(A=(97.6\pm 0.1)\%\) obtained with MLPC(ADAM). In conclusion, the tested routines showed excellent classification performances, making the technique a promising candidate for future applications in the diagnosis and grading of CS. Figure 4 reports the RBI associated with the prediction accuracy for the models examined as a function of wavenumber for all the classification problems of interest. In particular, we normalized RBI through the MinMax rule [63]. Specifically, MinMax normalization applied to the RBI had the function of highlighting the most relevant spectral components, allowing us to easily compare the RBI of the analyzed classifiers. We emphasize that the RBI provides a measure of the relevance of a spectral component in detecting the values of the label. In this sense, the behavior of RBI for MLPC (Figure 4a,c,e), characterized by the presence of a large number of peaks of similar intensities, indicated that the DL models studied rely on a large number of spectral components to reach the aforementioned classification performances. This trend is probably the result of the strongly non-linear nature of MLPC. On the other hand, the RBI of SVM and RFC, represented in Figure 4b,d,f, showed a small number of well-defined peaks in comparison to MLPC. Therefore, despite SVM and RFC showing worse classification performance than the DL models, they are potentially capable of providing more information about the  
biochemical mechanisms on the basis of the malignant degree of interest. In addition, this feature gives indications about the possibility of restricting the measured spectral interval to the Raman bands corresponding to the peaks of RBI, with negligible loss of classification performance but higher acquisition speed. By observing Figure 4b, we detected a peak of RBI at \(\sim\)602 cm\({}^{-1}\), exhibiting large feature importance both for SVM and for RFC. As shown in Table 1, this peak is attributable to phosphate groups (P-O bending) associated with hydroxyapatite. This result is in line with previous investigations, attributing the growing presence of bioapatites to the production of calcifications [64]. In Figure 4d, we report RBI as a function of the wavenumber for the G1-G2-G3 classification problem. In this case, a single prominent peak, attributable to Phe, can be observed both for SVM and RFC. In particular, by qualitatively analyzing the averaged Raman spectra in Figure 3b, an increase in the tumor progression coincided with a decrease in the Phe intensity. Finally, as expected, in the classification problem EC-G1-G2-G3, the behavior of the PFI (Figure 4f) appeared to be intermediate between the PFI in the EC-CS.