## 5 Discussion  
As mentioned in Section 2, there are a large number of publications in the literature on the use of deep learning systems in medical image classification, especially in histopathology. Image pre-processing is an important step, and as can be seen from the bibliography, there are a large number of alternatives for its implementation (in this paper we have used the most frequently presented ones in the literature). On the other hand, there are a large number of deep learning models in the literature, and to perform statistical analysis with great rigor and accuracy, all possible combinations of filters and models must be simulated (in several repetitions), the behavior analyzed, and the error rates measured. The computational cost and time required for each simulation are high. For this reason, it was decided to select these five models that have been widely used in the literature. However, to the best of our knowledge, there is no exhaustive statistical analysis in the literature that attempts to analyze what relevance or impact it has on the behavior of the system to use the different alternatives of deep learning models and preprocessing of histological images for the problem of breast cancer. As mentioned in Section 4, the analysis of the \(p\)-value in Table 6 yields a value of 0.146 for the filter technique and a value of 0.000 for the model of deep learning. This means that the choice of the different deep learning model alternatives has a statistically significant influence on the behavior of the system (measured by the AUC index). On the other hand, for the filter effect, it can be stated that it is not statistically significant, and therefore, the different methods have similar behavior to obtain the AUC value. This means that the designer of a deep learning system, for the problem of histopathological cancer images studied, must focus more attention on the deep learning model to be used, than on the processing systems used. The three homogeneous groups of filter types intersect each other, therefore, from a statistical point of view they are equivalent in terms of their behavior on the AUC output variable. It is also important to note that different convolution-based and histogram-based filter alternatives have been used. These alternatives, of these two major types of pre-processing, are mixed in the three homogeneous groups of Table 7. No statistically significant difference was found when using convolution-based or histogram-based types, both methods have similar behavior for the output variable. For the deep learning model type factor, there are also three groups, but, in this case, there are statistically significant differences between them. For this particular problem, and when analyzing and discussing the results, it can be seen that the group that achieves the best results (consisting of VGG16, VGG19, and ResNet50) are deep learning models that have a large number of parameters and therefore their size (measured in MB) and complexity is high. This does not carry over to the depth parameter (depth refers to the topological depth of the network, including activation layers, batch normalization layers, etc). As might be initially expected, VGG16 and VGG19 behave similarly from a statistical point of view, and both produce the best results. While it is true that both have a larger number of parameters out of the five deep learning models analyzed, their depth topology is still the lowest. As strengths of this paper, we must highlight the novelty and robustness of performing a comprehensive statistical analysis of the impact that the different pre-processing algorithms and deep learning models have on the classification of histopathological images in breast cancer. As a possible weakness of the study, we point out that it would have been interesting to analyze other models of deep learning systems, preprocessing, and even other pathologies.