## 3 Results
### Visualization of Filtered Anatomical Features  
This subsection focuses on investigating the feature activations of ballooned cells and fat droplets in all convolution layers for the \(\text{CNN}_{\text{SGDM}}\) and AlexNet models (Figure 7). This visualization tool could help physicians determine the most critical anatomical patterns that characterize the two liver diseases examined in this study. A key characteristic of each convolution filter is that it converts each image patch into multiple feature maps that are more similar to the filter itself [14]. These feature maps are then rectified by the ReLU function, ensuring that they always carry positive activation values. In the ReLU function, since any positive value can be assigned to the activated pixels, a division of the gradient tensor by its l2-norm is proposed, making the magnitude of the output normalized to a closed [0,1] interval [23]. This ensures that the magnitude of all activations is always within the same range of each previously convolved image, making the final representations more visually intense.  
Figure 6: Bar plots of accuracy, precision (PPV), recall (sensitivity) and specificity (TNR) characteristic values for various classification models including \(\text{CNN}_{\text{SGDM}}\), AlexNet, VGG-16 and a conventional Multilayer Perceptron Artificial Neural Network (MLP-ANN).  
Therefore, bright white pixels represent strong positive activations, while pure black pixels represent strong negative ones, respectively.  
As shown in Figure 7, it is found that in the two CNNs, the interest in the first ReLU\({}_{1}\) activations lies at identified edges, which can synthesize the basic structure of the balloon cell and fat droplet. It is recalled that both the CNN\({}_{\text{SGDM}}\) and AlexNet models apply the max pooling operation to their convolution layers (CNN\({}_{\text{SGDM}}\): layers 1, 2, AlexNet: layers 1, 2, 5). Unlike CNN\({}_{\text{SGDM}}\), AlexNet applies a \(3\times 3\) max pooling in all cases, which causes more blur in the two liver samples as it aims to reduce overfitting of the convolved pixel data. Based on the ReLU\({}_{2}\) activations, this technique is demonstrated to be efficient as it forces both neural networks to filter \"higher-level\" features that are less co-adapted and can lead to better generalization. Also in ReLU\({}_{2}\), it turns out that CNN\({}_{\text{SGDM}}\) executes an earlier activation of pixels that indicate swollen hepatocytes, while AlexNet chooses to perform additional filtering on the detected edges. Moving onto ReLU\({}_{3}\) activations, it is noted that non-informative pixel activations have been significantly reduced in both deep models, with AlexNet performing a more ideal filtering of the necessary curves that form the perimeter of the ballooned hepatocyte and the lipid droplet. The same model achieves also better performance within the ballooning area, as only the most important pixels of the two hepatocytes are activated.  
It is known that the AlexNet architecture consists of two additional convolution layers [21] which, according to the above figure, can lead to the activation of individual small patterns that could improve the overall classification performance. However, it seems that the first three convolution layers of CNN\({}_{\text{SGDM}}\) are sufficient for the necessary histological features to be filtered. On the other hand, a key prerequisite for CNN\({}_{\text{SGDM}}\) is to determine more optimal parameters which could further reduce the overfitting effect on the training data.  
Figure 7: Visualization of ReLU activations on CNN\({}_{\text{SGDM}}\) and AlexNet models. The CNN\({}_{\text{SGDM}}\) architecture consists of 3 convolution layers, while AlexNet of 5, respectively. The visualization focuses on the same ballooning and fat structures to determine the behavior of the two employed models during the filtering of image samples. In all cases, the brightest pixels denote the strongest activations indicating the most informative anatomical features.