# Does Two-Class Training Extract Real Features? A COVID-19 Case Study
## 4 Discussion
### Answering the Questions
However, if we look at the histograms of the images (bottom of Figure 4), we can more clearly distinguish some differences between them. For the displayed images, the COVID-19 image has a higher concentration of dark areas, while the healthy image has a higher concentration of light areas. In the case of pneumonia, it can be seen that the curve of the histogram is flatter, so that it has a more regular concentration than the other two cases. Even so, we cannot extract the characteristics from three images obtained randomly from the classes. It is true that there are clear differences in the histograms and that they could help in the classification of the DL system, but this does not answer why they are classified incorrectly if the differences are as clearly appreciable as those observed in the figure. In order to more clearly detect the characteristics of each class, a similar study must be carried out with all the images in the dataset. To achieve this goal, as we know that the relevant information could be concentrated in the histograms, the mean histograms of each class are calculated. These mean histograms show the mean of the occurrences of each value on the grayscale for each class and are presented in Figure 5.  
If we analyze more deeply the mean histograms, we can observe some characteristics that clearly distinguish each class:  
* COVID-19: This first class presents four important characteristics that can be easily appreciated (see Figure 5-left). They are detailed next:
* Pronounced peak of blacks. * Maximum concentration, between 150 and 200, with a local peak in the middle of the range. * Low concentration of whites. * Small end peak in whites. * Healthy: This second class presents four important characteristics as well (see Figure 5-right). They are detailed next:  
Figure 4: Image example from each class (after pre-processing) with its histograms. Figure 5: Mean histogram for each class. Low concentration of blacks. * Maximum concentration, between 100 and 150, with a local peak in the middle of the range. * Higher concentration of whites. * Small end peak in whites. * Pneumonia: This final class presents other characteristics that are similar to the ones detailed for the other two classes (see Figure 5-middle). They are detailed next: * Pronounced peak of blacks; similar to the COVID-19 class, but larger. * Maximum concentration, between 100 and 150, with a local peak in the middle of the range; exactly the same as the healthy class. * Higher concentration of whites than the COVID-19 class, but lower than the healthy class. * No end peak in whites. It can be seen that there are shared characteristics between classes. The two classes that have the most differences are COVID-19 and healthy (as might be expected), while the pneumonia class presents similar characteristics to the other two classes. Depending on which characteristics are taken into account by the trained model, it will resemble one or another class. Summarizing and generalizing the observed characteristics, we can distinguish: * Characteristic 1 (_Ch1_): Blacks' peak. * Characteristic 2 (_Ch2_): Whites' peak. * Characteristic 3 (_Ch3_): Black values' concentration. * Characteristic 4 (_Ch4_): White values' concentration. * Characteristic 5 (_Ch5_): Maximum concentration range. Thus, it would be interesting to study the consequences of these characteristics in the previously described models. Initially, a qualitative study is carried out on the possible characteristics used for each model, and based on these, we justify the results obtained in the various trained systems. According to the results shown in Table 5, where the class not included in the training was used as a test set, we can make the following observations: * H-P model: The characteristics that easily distinguish these classes are _Ch1_, _Ch2_, _Ch3_, and _Ch4_. We can theorize that these characteristics rule the classification result.