## 4 Experiment, Results and Discussion
### Experimental Data
As we can see, the internal and external clustering quality criteria, in some cases, contradict each other. This fact confirms that it is reasonable to apply the balance criterion which contains the internal and corresponding external criteria as the components. The balance criterion reaches its maximum value when dividing the set of GEP into three clusters. Moreover, according to the internal criterion, the optimal clustering corresponds to three clusters for subset A and two clusters for subset B. In accordance with the external criterion, the optimal clustering corresponds to the three-cluster structure. The next step of the model implementation is an application of a CNN to gene expression data in the allocated clusters. To confirm the previously described conclusions regarding the effectiveness of the optimal cluster structure formation based on clustering quality criteria, we studied cluster structures containing two, three, and four clusters. The simulation results are presented in Table 4. The analysis of the obtained results confirms the fact that the three-cluster structure is optimal in terms of both the classification accuracy and the value of the loss function when the CNN was training. However, it should be noted that the classification accuracy is quite high in all cases, which can be explained by the high efficiency of the CNN for this type of data and its resistance to the noise component. The classification accuracy of the studied objects was evaluated on the test data subset, which  
Figure 9: The simulation results regarding the practical implementation of the hierarchical spectral clustering algorithm based on inductive methods of complex systems analysis. was not used for the network's training. At the same time, in the case of a three-cluster structure, when using the third cluster containing 4964 genes, 100% classification accuracy was achieved with the minimum value of the loss function. When applying other clusters of this cluster structure, out of 39 objects that make up the test subset of gene expression data, 38 were identified correctly. The comparison analysis with other research in this subject area [1] allows us to draw conclusions on the performance of the proposed technique. So, in most cases presented in the review [1] a high classification accuracy is achieved when using a small number of genes. The proposed method allows us to form the subsets of differentially and co-expressed gene expression profiles, which contribute to the high value of the investigated samples' classification accuracy. Moreover, the allocated subsets of GEPs can be used as a next step in the hybrid modeling of disease diagnosis, such as various types of cancer, Alzheimer's, Parkinson's, etc., in order to take a more objective solution regarding the state of the patient using the object classification results obtained on various subsets of the allocated genes. In our minds, the presented research creates the conditions for increasing the objectivity of the diagnosis of the complex disease by making a compromise decision based on the results of the classification of objects containing informative differentially expressed and mutually correlated gene expression data, which are allocated in different clusters.