## 4 Application
### Visualization: Images and Convolutional Layer  
This section presents a visualization of the proposed architecture. These visualizations are presented in Figure 9. Unlike Figure 2, which is an executive summary with each position representing many samples, the visualizations in Figure 9 are sample-wise plots. In other words, the 10 original images that are sized 128 by 128 in panels A and B are the same samples in the second row (1 st Conv. Layer) and the third row (2 nd Conv. Layer). **Original Images in the 1 st Conv. Layer. ** The input images are sized 128 by 128. With the 1 st Conv. Layer constructed, we have \(61\times 61=3721\) new variables. We return to the same samples as shown in the first row in Figure 9 and use these 3721 variables only. When we plot these samples with these new variables, we resize them back in a 61 by 61 matrix form. Panel A represents the COVID class and panel B represents the non-COVID class. In addition, we use Model 1 in Table 10 to produce the texts that state the predicted probability of the COVID class. The red indicates the ground truth as COVID class (panel A) and the green indicates ground truth as non-COVID class (panel B). **1 st Conv. Layer. to 2 nd Conv. Layer. ** From the resulting matrix of the 1 st Conv. Layer, we are left with 3721 variables. We apply the proposed design in Table 10 and we create a new convolutional layer, i.e., the 2 nd Conv. Layer. This new layer has \(30\times 30=900\) variables. We take the same 10 sampled images from before and use these 900 variables to present these images. In this presentation, we resize these 900 variables into 30 by 30. In other words, we obtain a smaller matrix that is a smaller version with similar patterns as before. We use Model 4 to generate the predicted probabilities. These probabilities are printed on the top left corner of each image and they are color-coded similar as before (red probabilities indicate the ground truth of COVID class and green probabilities indicate the ground truth of non-COVID class). **Visualization Interpretation. ** The plot in Figure 9 of the original images for patients infected by COVID-19 has grey and cloudy textures in the chest area. Because an X-ray is at its brightest when most of the light beams emitted bounce back from the object, bones show as white and the margin is completely black. For muscle and organs inside the human body, X-rays that are emitted can only be partially collected; this causes the greyscale on the X-ray images in the chest area. For COVID-19 patients, there are grey and shaded areas in the chest X-rays. This is due to the inflammatory fluid produced when patients exhibit pneumonia-like symptoms. The fluid inside the chest area is a consequence of the human immune system fighting outside diseases. This shaded area (as seen in panel A in Figure 9) prevents us from observing clear areas in lungs. This is different in panel B, where the lung areas are dark and almost black, because a healthy lung is filled with air (i.e., the black present in normal cases' X-ray images). The black and white contrast in the two panels is directly related to how much inflammatory fluid is present in human lungs. This contrast translates to greyscale on pictures and is directly related to COVID and non-COVID cases (i.e., response variable \(Y\)). The same contrast can be seen using the new variables (these are \begin{table}
\begin{tabular}{l c c} \hline \hline
**Model** & **AUC (Test Set)** & **No. of Parameters** \\ \hline Proposed: & & \\ ICNN (Parameters: \{starting point: 6, window size: 2 by 2, stride: 2\}) & 0.97 & 12,000 \\ ICNN (Parameters: \{starting point: 4, window size: 3 by 3, stride: 3\}) & 0.98 & 13,000 \\ Average & 0.975 & 12,500 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Multiclass lung cancer variants diagnosis: the experiment results for multiclass lung cancer variants classification. In total, there are 4 classes (0: healthy, 1: COVID-19, 2: pneumonia, and 3: tuberculosis).