# Adversarial Validation in Image Classification Datasets by Means of Cumulative Spectral Gradient
## 4 Results and Discussion
### MNIST Dataset  
The results for the 160 validations performed on the MNIST dataset are shown in Figure 5. The first case shows the results ordered according to the CSG metric and its respective relationship with data separability (Figure 5a), where each column shows the result of the adversarial validation, represented by the value of the CSG metric for a given class (classes 0 to 9 in MNIST represented in a shade of blue) for each type of transformation. On the other hand, Figure 5b shows the variability of the interclass CSG metric for each type of modification.  
According to Figure 5a, for the MNIST dataset, there are modifications where the data are not easily separable from the original data, implying that the distribution of these modified data deviates very little from the original distribution. This is the case for noise addition modifications (impulse noise and shot noise), as well as the addition of splotches (spatter) and dotted lines to the MNIST images, which do not generate a significant impact. The latter are closely followed by the modification that adds zigzags to the image, in a controlled way, thanks to the modification that adapts the brightness of each straight segment.  
In addition, in Figure 5a, it is observed that affine transformations such as shear and rotate reach values that slightly exceed the 50 th percentile of the metric, but other transformations that may involve loss of information such as translation and scaling cause the distribution of the modified data to move away from the distribution of the original data (CSG metric close to zero). It is also observed that distortions such as blurring and edge-only images do not help to preserve data with a distribution similar to that of the original data. Finally, in the MNIST-C dataset, the distortions of blurring, brightness and the inversion of the pixel values (stripe) completely distance the distribution of the modified data from the distribution of the original data (CSG \(\approx\) 0).  
On the other hand, the analysis of the results by class in the MNIST dataset shows that there are modifications in which the results between classes are consistent (see Figure 5b). This tendency is present in modifications with high CSG values (CSG \(\geq\) 0.9 for all classes) as is the case of impulse noise, spatter, dotted line and shot noise. It is also possible to find consistent modifications with low CSG values (CSG \(\leq\) 0.1 for all classes) as in the case of impulse noise, spatter, dotted line and shot noise.  
However, some modifications were found where the results of the CSG metric varied considerably between classes (see Figure 5b). For example, the modification of zigzag addition to an image presents a difference of 0.54 between the class with the highest CSG value (class 0) and the class with the lowest CSG value (class 1). Other modifications with inter-class variability correspond to rotation (difference of 0.35 between class 0 (high) and class 7 (low)), Canny filter (difference of 0.34 between class 5 (high) and class 1 (low)) and shear transformation (difference of 0.25 between class 4 (high) and class 3 (low)). This means that there are corruptions that affect some classes more than others.