br Using the algorithms that extract the
Using the algorithms that extract the evidence degrees and the ef-fects of contradiction, the paraconsistent patterns for normal Apicidin tissue (NO), non-melanoma skin tissue (BCC + SCC), and pre-cancerous skin tissue (AK) were created. Fig. 4 shows the graphs of the paraconsistent patterns (PPμE NO, PPμE (BCC + SCC), and PPμE AK) obtained in this study.
4.2. Tests with histopathological groups
For testing with the arrangement of the histopathological groups, two investigation methods were employed. The first was Mode 1 (no cross-validation), in which the Raman database's total skin cancer samples were used to construct the paraconsistent patterns of the array (NO, [BCC + SCC], AK), and then all the samples were tested.
Fig. 4. Graphs of the Raman intensity paraconsistent patterns.
(A) histopathological group of normal skin without lesions (PPμE NO), (B) histopathological group of basal cell carcinoma and squamous cell carcinoma (PPμE BCC + SCC), and (C) histopathological group of actinic keratosis (PPμE AK).
The second method was Mode 2 (with cross-validation). In this mode, the k-fold cross-validation technique [28,29] was used. In this technique, a portion of the total database samples (subset) was removed to form the patterns, and the hits tests were conducted with the re-maining part. The procedures for separating part of the samples for pattern generation and testing with the remaining part were followed until the entire database was addressed. The final result obtained by this analysis was the average percentage of correct answers in each procedure [28,29].
4.3. Test arrangement type for Mode 1
Considering this type of sample distribution, a total of 30 normal tissue samples, 57 AK tumor lesion tissue samples, and 136 samples comprising BCC and SCC malignant lesions tissues were collected.
Fig. 5 shows the results of the SPA-PAL2v test using process Mode 1 (without cross-validation) for this type of arrangement, whereby a random sample (no. 162, Fig. 5a) was selected from the 223 samples available from the Raman database.
The Raman intensity (μA) of the sample was greater than 0.5 (es-tablished cutoﬀ value) in the study involving each established pattern (NO, [BCC + SCC], and AK).
Above the representation of each figure is also recorded the occur-rence of the respective points greater than 0.5 and the evidence degree of frequency calculated by the SPA-PAL2v. For the NO group, the evi-dence degree of frequency μFr = 0.23068; for the BCC + SCC group, μFr = 0.38884; and for the AK group, μFr = 0.38068.
By comparing the values of the evidence degree of frequency, we conclude that sample no. 162 belongs to the BCC + SCC arrangement because it has the highest μFr value, consequently characterizing the diagnosis in that group.
Table 2 presents the test results, which include the correct grouping and error; the percentages of correct classification for the NO group, BCC + SCC group, and AK group; and the total arrangement obtained in the final tests for Mode 1 (without cross-validation) process.
4.4. Tests of arrangement types for Mode 2 (with cross-validation)
In this mode, the k-fold cross-validation technique was used, in which 20% of the total skin cancer tissue samples from the database were taken to constitute the subset of sample data selected for the tests. With the remainder, that is, 80% of the samples, the subsets used for the construction of the paraconsistent patterns related to each histopatho-logical group arrangement were obtained. Considering that 20% of the samples were used in each analysis to form the sample data selected for the tests, the test procedures were repeated five times to cover the total samples of the Raman database.
Table 3 presents the results with the correct grouping and errors, the partial accuracies in the five subsets of the samples that were tested using the cross-validation method in the arrangement (NO × [BCC + SCC] × AK), and the global accuracy.
4.5. Comparison of SPA-PAL2v results with PCA
In this work, analyses were performed using PCA and discriminant analysis (PCA/DA) applied to the principal components scores in the same Raman spectral database (ex vivo skin tissue samples) and the same histopathological group (NO × [BCC + SCC] × AK).
Table 4 presents the results obtained by the statistical methods of PCA/DA and the results obtained with SPA-PAL2v in Mode 1 (no cross-validation) and Mode 2 (with cross-validation).
In the initial test, the graphs of the paraconsistent patterns of each histopathological group studied (NO, [BCC + SCC], AK) were obtained. Fig. 4 highlights the profile and amplitude diﬀerence of the NO group in relation to the other two groups, (BCC + SCC) and AK, throughout the Raman wavelength range. For example, between the Raman wave-lengths of 1200 and 1400 cm−1, the (BCC + SCC) and AK groups had diﬀerent profiles and amplitudes from the NO group, according to the graphical results.