## 3 Results
### Testing Results  
To test the reliability of the developed methodology, the two-trained models (\(\text{CNN}_{\text{Adam}}\) and \(\text{CNN}_{\text{SGDM}}\)) are called to identify 40 unknown liver structures (10 per class). In the current task, the softmax function is asked to assign an input image described by a vector x, to a class identified by a class label y \(\in\) {ballooning, fat, sinusoid, vein}. Thus, the function outputs a probability distribution value for the four classes within a [0,1] confidence interval. After the end of the testing process the purpose is (a) to measure the classification accuracy for every individual liver class and (b) retrieve further statistics from the classification report. These metrics include the mean accuracy, precision, recall (sensitivity) and F-score (Table 1).  
Examples of the image patch test results are shown in Figure 5. Each of these images is accompanied by its estimated classification probability (%), indicating how confident the CNNs are of their predictions. According to the figure, in most cases, an accurate discrimination result marked by a green frame is presented for the four hepatic tissue objects. It is observed that both neural networks have a reduced efficiency in identifying some sinusoids (red frames = misclassifications), which are among the most complex histological features to classify. However, the success lies in the fact that all ballooned cells and fat droplets, which characterize two of the most widespread liver diseases, have been identified with high confidence levels. Based on the exported percentages in Table 1, it is clear that the classifiers are more stable in detecting ballooned hepatocytes, as these consist of multiple changes in the values of their adjacent pixels. They also successfully achieve a visual discrimination of circular structures not always referred to as steatotic fat cells, but as hepatic veins, because they tend to contain several red blood cells.  
Proceeding to Table 1, additional information is provided for the two classifiers, with the mean precision and recall (sensitivity) values. First, the performance of \(\text{CNN}_{\text{Adam}}\) shows a lower recall value (92.5%) compared to higher precision (93.6%). This indicates that \(\text{CNN}_{\text{Adam}}\) failed in some true positive (TP) samples. Consequently, it produced more false negative (FN) diagnostics and less false positive (FP) ones, respectively. Examples of \(\text{CNN}_{\text{Adam}}\) misclassifications are shown in Figure 5 below, in which two incorrect sinusoid characterizations are displayed. In contrast, \(\text{CNN}_{\text{SGDM}}\) delivered balanced precision and recall rates (95%), by producing more true positives (TP). For verification purposes, the two measures are combined into a single F-score (F1-score) value, representing their harmonic mean. Thus, if one metric carries a lower value, the F-score converges closer to the small number than the large one, which gives the classification models a more appropriate score than a common arithmetic mean. \(\text{CNN}_{\text{[PERSON]}}\) then receives a 93% F-score, whereas \(\text{CNN}_{\text{SGDM}}\) a higher 95% F-score due to its fully balanced performance.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Deep** \\ **Model** \\ \end{tabular} } & \multicolumn{6}{c}{**Classification Results (\%)**} \\ \cline{2-10}  & \multicolumn{4}{c}{**Liver Class Accuracy**} & \multicolumn{4}{c}{**Mean Performance Metrics 1**} \\ \cline{2-10}  & **Ballooning** & **Fat** & **Sinusoid** & **Vein** & **Accuracy** & **Precision** & **Recall** & **F-Score** \\ \hline \(\text{CNN}_{\text{Adam}}\) & 100 & 100 & 70 & 100 & 92.5 & 93.6 & 92.5 & 93 \\ \(\text{CNN}_{\text{SGDM}}\) & 90 & 100 & 90 & 100 & 95 & 95 & 95 & 95 \\ \hline \hline \end{tabular}  
* Mean classification values for \(\text{CNN}_{\text{Adam}}\) and \(\text{CNN}_{\text{SGDM}}\) models.  
\end{table}
Table 1: Classification report from the initial conducted experiments.