## 4 Discussion  
The results obtained from this new methodology for classifying skin lesions by employing eleven artificial intelligence algorithms using concatenated signatures were promising. This methodology proposes using several integral transforms (Fourier, Mellin, and Hilbert) along with the uniform LBP method of texture features to obtain a series of concatenated signatures for each lesion. This methodology works quite well for those images of skin lesions that lack noise. It is important to note that the concatenation of the signatures was achieved using the three color spaces (RGB) and the gray image to extract as much information as possible. This allows the artificial intelligence algorithms to detect the most subtle differences between the lesions. The eleven tables show excellent results for the  
Figure 5: ROC curve for one example subspace k-NN process. (**a**) Training ROC. (**b**) Testing ROC. Figure 6: Confusion matrix for one example subspace k-NN process: (**a**) training, (**b**) testing. accuracy, sensitivity, specificity, and precision metrics of the method, both for the training set and the test set. The group of lesions used to test this methodology was absent in the set of images used to train the various artificial intelligence algorithms. For both the training and test sets, the algorithms were run 30 times, thus obtaining an average and a \(\pm\)standard deviation for each case. When defining the best classifier from the eleven presented in this work for this class of images, we observed that the classifier with the best performance was the subspace k-NN classifier, which had the best results for the test set. The same happens when we compare the metrics regarding the training of the various classifiers. The remaining ten classifiers also performed well. Using these classifiers when the input consists of concatenated signatures that are invariant to rotation, scale, and translation is an excellent contribution to this work. This work aligns with previous studies on the classification of skin lesions using artificial intelligence algorithms. For example, ref. [38] presented a dataset of 2241 histopathological images from 2008 to 2018. They employed two deep learning architectures, namely VGG19 and ResNet50. The results showed a high accuracy for distinguishing melanoma from nevi, with an average F1 score of 0.89, a sensitivity of 0.92, a specificity of 0.94, and an AUC of 0.98. In reference [39], the authors present an automated skin lesion detection and classification technique utilizing an optimized stacked sparse autoencoder (OSSAE)-based feature extractor with a backpropagation neural network (BPNN), named the OSSAE-BPNN technique, that reached a testing accuracy of 0.947, a sensitivity of 0.824, a specificity of 0.974, and a precision of 0.830. More studies in these areas are described in Table 13. Table 13 compares our work with other approaches, and our results are generally better. However, the results show that training and validation data metrics are around 99%. The signatures are invariant to each image's rotation, scale, and displacement. These studies demonstrate the potential of artificial intelligence algorithms in the classification of skin lesions, and this work furthers our understanding of how to achieve the best results. Our methodology is a breakthrough in classifying skin lesions using artificial intelligence algorithms and concatenated signatures. Indeed, the main contribution of this manuscript is how the images have been converted into linked signatures using the different integral transforms mentioned above, as well as the uniform LBP vectors. This is a promising development in medical diagnosis and has the potential to revolutionize how medical professionals diagnose and treat skin lesions. It is worth mentioning that concatenated signatures cannot only be used for classifying skin lesions; they can be used for other medical imaging tasks, such as identifying tumors or categorizing brain scans.