## 7 Results  
The proposed methodology was implemented in MatLab 2019b on an HP computer, Intel Core i5, 12 GB RAM. A total of four experiments were done. The ISIC archive-2019 had a significant imbalance between the majority and minority classes. To handle imbalanced classes, we used the ensemble method using three classifiers with a linear plurality vote. In Exp-1 and Exp-2, the performance metrics reported were for the dataset without splitting. In Exp-3 and Exp-4, the dataset was randomly sampled five times with replacement in 70% for the training part and 30% for the test. Since the original set was sampled with replacement, some elements were repeated in the training sets, and others were not presented. With the five sets, we trained the classifiers, and thus we obtained different predictions that helped us have a fair classification of the images. In the first experiment (Exp-1), the complete dataset was used, the 25,331 dermoscopy color-images of the ISIC archive-2019. The \(\alpha\) parameter in the fractal signature was varied from \(\alpha=-2\) to 2 with stride 0.1. The best performance was obtained with \(\alpha=-2.0\). Table 2 displays the confusion matrix output for the Exp-1 with \(\alpha=-2.0\). The ISIC 2019 library had 867 AK, 3323 BCC, 628 SCC, 2624 BKL, 4522 MEL, 12875 NEV, 239 DER, 253 VASC. The computer-aided diagnosis response was 802 AK, 3956 BCC, 295 SCC, 2285 BKL, 3746 MEL, 14,105 NEV, 48 DER, 94 VASC. As was expected, the classes with an insufficient number of images were misclassified, like SCC, DER, and VASC. We must always keep in mind to have a representative dataset \(\mathbf{D}_{\mathcal{C}}\) for the class \(\mathcal{C}\) that allows us to reproduce or generate the space for that class. For \(\mathbf{D}_{\mathcal{C}}\), all the images in \(\mathcal{C}\) should be rewritten as a linear combination of the elements in \(\mathbf{D}_{\mathcal{C}}\), which was not happening with the classes SCC, DER, and VASC. Based on the confusion matrix in Table 2, the true positive \(TP\), false positive \(FP\), false negative \(FN\), and true negative \(TN\) values were computed, as shown in Table 3. These values were used in Equations (18) to (21) to compute the performance of the computer-aided diagnosis of the Exp-1. Table 4 shows the percentage of the values per class of accuracy, precision, sensitivity, and specificity. As was expected, sensitivity was low due to poor representation of SCC, DER, and VASC images. The Exp-1 computer-aided diagnosis yielded a mean \(\pm\) standard deviation for \(accuracy=97.35\pm 2.04\%\), \(precision=91.61\pm 6.89\%\), \(sensitivity=66.45\pm 29.09\%\), and \(specificity=97.85\pm 3.98\%\). Experiment 2 (Exp-2) used a dataset of 24,839 images with 867 AK, 3323 BCC, 628 SCC, 2624 BKL, 4522 MEL, and 12,875 NEV. The 239 DER and 253 VASC images were not considered. Again, the \(\alpha\) parameter in the fractal signature was varied from \(\alpha=-2\) to 2 with stride 0.1. The best performance was obtained with \(\alpha~{}=~{}-1.9\). For the Exp-2, the mean \(\pm\) standard deviation of the computer-aided diagnosis was \(accuracy=96.85\pm 1.71\%\), \(precision=90.12\pm 6.07\%\), \(sensitivity=79.25\pm 19.06\%\), and \(specificity=97.42\pm 3.93\%\), as shown in Table 5. As is observed, when not considering the classes with very few images, the sensitivity increased, and the standard deviation decreased. So this confirmed the importance of having a good sampling for each of the classes. For experiment 3 (Exp-3), the ISIC dataset of 25,331 dermoscopy color-images was randomly divided into 70% for the training dataset (17732 images) and 30% for the test dataset (7599 images). The \(\alpha\) parameter in the fractal signature was varied from \(\alpha=-2\) to 2 with stride 0.1. The best performance was obtained with \(\alpha~{}=~{}0.4\).