## 4 Experimental Results and Discussion
### Relevance of Sectors According to Shapley Values  
Glaucoma is characterized by a progressive enlargement of the optic cup area, leading to a narrowing of the neuroretinal rim [12]. Although this enlargement can occur in all directions, certain regions tend to be affected earlier than others. In eyes with mild glaucomatous damage, rim loss predominantly appears in the temporal inferior and temporal superior regions. As the disease advances to a moderate stage, the temporal region typically shows the most significant rim loss. In cases of severe glaucoma, the nasal disc area generally experiences the least rim loss, while the nasal inferior region tends to be more affected than the nasal superior region.  
With this in mind, Shapley values have been calculated for the different sectors in order to assess in this section the degree of coincidence with the expected values from a medical point of view. For this purpose, a global relevance measure has been obtained for each sector, which indicates the probability that the maximum of the contributions provided by the Shapley values for a given image is found in that sector. More specifically, given the models trained for a specific network architecture (all the partitions have been  
Figure 7: Boxplots showing the correlation coefficients between Shapley values for each pair of architectures: VGG19 (v19), ResNet50 (r50), InceptionV3 (i3), and Xception (xcp).  
considered as a whole) and a given test set, each sector has a global probability of \(N\%\) of being the most relevant, i.e., the one that contributes the most for an input image, according to the Shapley values obtained for a normal or glaucoma prediction. In this sense, in the case of a normal prediction, the signs of the Shapley values were inverted to study the distribution of these values and their averages. The results obtained are shown in Figure 8.  
What stands out the most in this figure is the predominance of the background (B) sector, being the most probable sector in most cases, although with some differences between classes. For the VGG19 and ResNet50 architectures, the probabilities assigned to the B sector are the highest in the case of a normal prediction. However, in the case of a glaucoma prediction, the highest predictions assigned to the B sector are found for the InceptionV3 and Xception architectures. This extremely high relevance of the B sector may seem very surprising from a medical perspective but in this regard, it is worth recalling the study carried out by [2] where they showed that the information contained in the background may allow the detection of glaucoma in this type of models.  
In Figures 9 and 10 we can see, respectively, the average Shapley values per class and their dispersion. We show only the results for the partitions that obtained the highest balanced accuracy per architecture for the re-trained  
Figure 9: Average Shapley values per architecture, for each sector, for the folds with the highest balanced accuracy. The results are separated according to the class predicted by the network.  
Figure 10: Dispersion of Shapley values per architecture, for each sector, for the folds with the highest balanced accuracy. The results are separated according to the class predicted by the network. For each image in the test set, a dot is shown on the graph indicating the Shapley value for each sector. If any point overlaps with a point in another image in the same sector, it is shifted slightly on the y-axis.