## 3 Material and Methods  
Conceptual Description of the Hybrid Model to Form Subsets of Differentially Expressed and Mutually Correlated GEPs Based on the Joint Application of Clustering Algorithms and CNN  
As was noted in the introduction, the main goal of this research is to increase the objectivity of forming subsets of differentially expressed and mutually correlated GEPs, which creates the conditions for increasing the accuracy of the classification of objects whose attributes are the selected gene expression values. The application of the clustering stage allows the division of the set of gene expression profiles into subsets that are mutually close by the appropriate metrics, and the choice of the metrics by which the clusters are formed is very important. In [2], various metrics focused on evaluating the proximity level of high-dimensional GEPs were investigated, and as a result of the research, a hybrid metric based on the joint application of metrics based on the assessment of mutual information and [PERSON]'s chi-squared test was proposed. This metric is used to form a cluster structure within the framework of our research. Figure 1 shows the structural block chart of the stepwise procedure of the general concept to form the subsets of differentially expressed and mutually correlated GEPs based on the joint application of clustering and classification methods. The practical implementation of this concept involves the following stages:  
1. Removing non-expressed and low-expressed gene expression profiles. The implementation of this step assumes the removing of genes with zero expression for all samples and non-informative genes by the absolute value of gene expressions, variance, and Shannon entropy. 2. Dividing the subset of the gene expression profiles formed in stage I into two equivalent subsets with subsequent parallel clustering on these data subsets within the range of the clustering algorithm's variation parameter. The final decision regarding the optimal parameters of the corresponding clustering algorithm operation is performed taking into account the analysis of the values of the balance criterion, which contains, as the components, both the internal and external clustering quality criteria. The optimal cluster structures correspond to the maxima values of the balance criterion. 3. Classification of objects containing gene expression data in the selected clusters by applying a one-dimensional two-layer convolutional neural network (CNN). At this stage, a CNN is applied to the gene expression data of each cluster in order to classify the examined objects. The implementation of this stage requires preprocessing of gene expression value vectors in order to set the filters correctly. Vectors of gene expressions are supplemented with genes with zero expression so that the length  
Figure 1: Structural block chart of the stepwise procedure for implementing the concept to form the subsets of differentially expressed and mutually correlated GEPs. of the gene expression vector is divided without residuals by the filter size. The classification stage results in calculation of the classification quality criteria based on the gene expression data allocated in each of the clusters. 4. Analysis of the obtained results and formation of subsets of differentially expressed and mutually correlated GEPs. The implementation of this stage involves a comprehensive analysis of both the clustering and classification quality criteria. The subsets of gene expression data that correspond to the maximum values of both the clustering and classification criteria are allocated at this step. It should be noted that this stage's implementation assumes the formation of several subsets of differentially expressed and mutually correlated gene expression profiles according to the maximum values of the relevant criteria.