## 4 Applying Convolutional Neural Network (CNN) to Gene Expression Data in Formed Clusters  
Within the framework of the simulation process, we utilized a one-dimensional two-layer convolutional neural network to classify objects using gene expression data attributes in the formed clusters. The structure of the network and hyperparameter values were chosen based on the authors' previous studies, as presented in [26]. The kernel size was set to 8, and the dense layer density was 256. The filter parameters for different cluster structures of the gene expression data are shown in Table 2. Similarly to their previous model, the authors divided the set of objects under investigation (3269) into three subsets. Whereby, 65% of the objects (2125) were used for training and validation, while 35% (1144) were used for testing. In this case, 70% of the objects from the first subset (1487) were used for network training, and 30% (638) were used for model validation. Quality assessment of the model was performed by evaluating the nature of the changes in classification accuracy and loss function during the CNN training process, which were calculated with subsets of gene expression data used directly for training and validating the model. The adequacy of the model was evaluated by applying test data, with the calculation of classification quality criteria. Figures 4-6 depicts the distribution characteristics of the respective classification quality criteria for samples calculated during modeling, when identifying the presence or absence of the corresponding disease using the gene expression data located in the highlighted clusters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{Layer} & \multicolumn{3}{c}{Three-cluster structure} & \multicolumn{3}{c}{Four-cluster structure} \\  & Cl.1 & Cl.2 & Cl.3 & Cl.1 & Cl.2 & Cl.3 & CL.4 \\ \hline
1 & \(108\times 50\) & \(133\times 50\) & \(49\times 50\) & \(102\times 50\) & \(71\times 50\) & \(49\times 50\) & \(69\times 50\) \\ \hline
2 & \(216\times 25\) & \(266\times 25\) & \(98\times 25\) & \(204\times 25\) & \(142\times 25\) & \(98\times 25\) & \(138\times 25\) \\ \hline \multirow{2}{*}{Layer} & \multicolumn{3}{c}{Five-cluster structure} \\  & Cl.1 & Cl.2 & Cl.3 & CL.4 & CL.5 & \\ \hline
1 & \(96\times 50\) & \(12\times 50\) & \(89\times 50\) & \(54\times 50\) & \(40\times 50\) & \\ \hline
2 & \(192\times 25\) & \(24\times 25\) & \(198\times 25\) & \(108\times 25\) & \(80\times 25\) & \\ \hline \multirow{2}{*}{Layer} & \multicolumn{3}{c}{Six-cluster structure} \\  & Cl.1 & Cl.2 & Cl.3 & CL.4 & CL.5 & CL.6 \\ \hline
1 & \(58\times 50\) & \(60\times 50\) & \(54\times 50\) & \(34\times 50\) & \(31\times 50\) & \(55\times 50\) \\ \hline
2 & \(116\times 25\) & \(120\times 25\) & \(108\times 25\) & \(68\times 25\) & \(62\times 25\) & \(110\times 25\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the filters used in the one-dimensional two-layer CNN. Figure 4: Distribution diagrams of classification quality criteria values for samples of patients with ACC and GBM cancer, when using gene expression data from different clusters  
Figure 5: Distribution diagrams of classification quality criteria values for samples of patients with KIRC, LGG, LUAD, and LUSC cancer, when using gene expression data from different clusters. Analysis of the obtained results allowed us to identify a high convergence of the clustering quality criteria, the distribution of which for the obtained cluster structures is presented in Figure 2. It should be noted that, in almost all cases, the accuracy of sample classification was quite high, while in each cluster structure, one cluster of gene expression profiles could be distinguished, the application of which resulted in a lower classification accuracy compared to the other cases. According to the clustering criteria presented in Figure 2, the four- and six-cluster structures are optimal. According to the classification quality criteria, the four-cluster structure was the most stable for all types of sample studied.