## 3 Material and Methods
### A Hybrid Inductive Model of GEP Clustering Based on the SOTA Clustering Algorithm  
As was noted in the introduction, the self-organizing SOTA clustering algorithm [3] forms a binary topological tree based on the joint use of self-organizing [PERSON]'s maps [4] and the Fritzke algorithm of spatial cellular structure growth [5]. The application of this algorithm leads to an increase in the number of tree nodes in the higher object (gene expression profiles) density areas, while the concentration of objects in the area with lower density does not change at the current step of the algorithm application. An analysis of the simulation results presented by the authors of the SOTA clustering algorithm [3] has shown that the result of the algorithm operation (the structure of the formed topological tree) is determined by the boundary value of the relative change of the variation coefficient value or by the number of iterations on the one hand, and by the value of the parameter for correcting the weights of the sister's cell (parameters for correcting other cells are determined using the conditions: \(\alpha_{w}=2\alpha_{p};\ \alpha_{p}=5\alpha_{s}\) ). Within the framework of our research, the boundary value of the relative change of the variation coefficient was taken as 0. Under this condition, the termination of the algorithm's operation was determined either by repeating the nature of the GEP distribution into clusters on two consecutive iterations or by reaching the boundary number of iterations. Determination of the optimal value of the parameter for correcting of the sister's cell weights was performed using the previously described OCIT. The implementation of the inductive hybrid model of the SOTA algorithm assumes the following stages:  
1. Data formation and initialization of the SOTA clustering algorithm. 1.1 Formation of a matrix of gene expression data, where the rows are the investigated objects, and the columns are the genes whose expression values determine the state of the corresponding object. 1.2 Removal of the non-informative GEPs in terms of statistical criteria and Shannon entropy in accordance with the technique presented in Section 3.2. 1.3 Formation of metrics for assessing the proximity level of GEP. Considering the research results presented in [2], we have used a hybrid modified metric based on the integrated application of the hybrid metric of mutual information maximization and [PERSON]'s chi-squared test. 1.4 Formation of two equivalent subsets of GEPs \(A\) and \(B\). 1.5 Formation of clustering quality criteria to assess the quality of the cluster structure. 1.6 Initialization of the algorithm. The boundary value of the relative change of the variation coefficient \(E_{lim}=0\) and the range and step variation of the parameter \(\alpha_{s}\) for the correction of the sister's cell weight are set up. 2. GEP clustering and determination of the SOTA algorithm's optimal parameters. 2.1 Initialization of the first value of the parameter for correcting the sister's cell weights: \(\alpha_{s}=\alpha_{smin}\). 2.2. Applying the SOTA clustering algorithm to GEP contained in equivalent subsets A and B. Cluster structure formation. 2.3. If the number of clusters formed on equivalent subsets \(A\) and \(B\) is the same, then, the calculation of both the internal and external clustering quality criteria and the increase in the \(\alpha_{s}\) value is \(\alpha_{s}=\alpha_{s}+d\alpha_{s}\). Otherwise, increase the \(\alpha_{s}\) without calculating the criteria. 2.4. If \(\alpha_{s}\leq\alpha_{smax}\), then, go to step 2.2 of this procedure. Otherwise, use the calculation of the balance criterion values. 2.5. Analysis of the obtained results and fixing the values of the \(\alpha_{s}\) parameter, which correspond to the maximum values of the balance criterion. 2.6. Application of the SOTA clustering algorithm with optimal value of \(\alpha_{s}\) parameters to the full set of GEPs created at step 1.2 of this procedure and formation of a cluster structure. 3.