## 3 Material and Methods  
### Experimental Dataset Formation and Preprocessing  
During the simulation process, gene expression data from The Cancer Genome Atlas (TCGA) [22], obtained by applying RNA sequencing on the Illumina platform [23], were used. Each initial data sample contained 19,947 types of genes as attributes, where the expression of each gene was determined by its activity level, which was proportional to the amount of the corresponding gene type. The experimental dataset contained nine types of data, eight of which corresponded to eight types of cancer, while the ninth type of data corresponded to samples for which no cancerous tumor was identified based on clinical trials. The total number of samples studied was 3269. Thus, at the initial stage of modeling, the gene expression matrix had the following form: \(E=(3269\times 19,947)\). The classification of the experimental data used in the modeling process is presented in Table 1.  
At the initial stage, we removed uninformative gene expression profiles based on their absolute expression values, variance, and Shannon entropy, as outlined in [24]. This process resulted in the removal of 4814 gene expression profiles, resulting in a filtered gene expression value matrix in the following form: \(E=(3269\times 14,451)\). These data were used in our research. Application of an Objective Clustering Inductive Model Based on the Spectral Clustering Algorithm for Forming Subsets of Differentially Expressed and Mutually Correlated Gene Expression Profiles  
We believe that the objectivity of identifying the object state can be enhanced by parallelizing the process of processing gene expression data. This can be achieved by forming subsets of differentially expressed and mutually correlated gene expression profiles, followed by classifying objects containing gene expression data in the selected clusters. The final decision is reached by analyzing the classification results of all clusters using an alternative voting system. Figure 1 shows a structural block diagram for implementing this procedure. The initial stage of the procedure illustrated in Figure 1 involves forming subsets of mutually correlated and differentially expressed gene expression profiles, by applying the inductive spectral clustering algorithm. The algorithm's effectiveness for high-dimensional gene expression profiles clustering was demonstrated in [9]. To evaluate the proximity of gene expression profiles and clusters within the current modeling framework, we used a hybrid metric of gene expression profile proximity, based on mutual information maximization using various entropy calculation methods. The modified proximity metric is described in [7]. The minimum value obtained using this metric corresponds to the minimum distance between the corresponding gene expression profiles. Additionally, we employed this modified metric to estimate the closeness of gene expression profiles, clusters, and gene expression profiles and clusters. \begin{table}
\begin{tabular}{c c c} \hline
**No** & **Type of Cancer** & **Number of Samples** \\ \hline
1 & Adrenocortical carcinoma—ACC & 79 \\
2 & Glioblastoma multiforme—GBM & 169 \\
3 & Sarcoma—SARC & 263 \\
4 & Lung squamous cell carcinoma—LUSC & 502 \\
5 & Lung adenocarcinoma—LUAD & 541 \\
6 & Stomach adenocarcinoma—STAD & 415 \\
7 & Kidney renal clear cell carcinoma—KIRC & 542 \\
8 & Brain lower-grade glioma—LGG & 534 \\
9 & Normal & 224 \\ \hline \end{tabular}
\end{table} 
Table 1: The classification of experimental gene expression data used in the modeling process  
Figure 1: Structural block diagram illustrating the step-by-step procedure for processing gene expression data in the diagnostic system of the investigated object. The internal quality criterion used for clustering gene expression profiles considered, the distribution within individual clusters in relation to the corresponding cluster's median and the distribution of individual clusters (medians) in the feature space.