A stepwise procedure implementation of this algorithm is possible; however, in this case there arises the problem of the optimal cluster structure formation. Internal clustering quality criteria can allow us to form an optimal cluster structure, but they do not solve the reproducibility error. Successful results obtained in one dataset do not guarantee obtaining the same results when using other similar datasets. Another clustering algorithm used for gene expression data clustering is the spectral clustering algorithm [6; 7; 8; 9]. This algorithm is one of the modern algorithms which allows us to identify clusters of arbitrary shape based on the application of object similarity matrices. In comparison with traditional algorithms, the spectral clustering algorithm has many fundamental advantages. The results obtained by applying the spectral clustering algorithm are often superior in quality to those obtained using traditional approaches. Moreover, the implementation of the spectral clustering algorithm is straightforward and can be effectively implemented based on the methods of standard linear algebra. The general difference of the spectral clustering algorithm is that the formation of clusters is not based on the absolute location of objects in the feature space, but instead on the basis of the analysis of the level of these objects' affinity, which is especially useful when forming clusters with complex shapes. The principal problem in the successful implementation of the spectral clustering algorithm is the formation of the optimal cluster structure according to both the relevant clustering quality criteria and the reproducibility error. It should be noted that this problem does not currently have an unequivocal solution. In this research, we present our point of view to solve this problem solution. We propose a hybrid inductive model of the stepwise procedure to form differentially and co-expressed gene expression profiles based on the joint use of statistical and entropy criteria, spectral and SOTA clustering algorithms implemented within the framework of objective clustering inductive technology, and convolutional neural networks for obtaining the final solution concerning the choice of optimal cluster structure. The main contributions of this manuscript are the following:  
* We propose a technique to form a subset of informative GEPs based on the joint use of statistical criteria and Shannon entropy, where the final solution regarding the level of respective gene informativity is conducted based on analysis of the general Harrington desirability index. * We implemented the SOTA and spectral clustering algorithms within the framework of objective clustering inductive technology, which allows us to decrease reproducibility error when the gene expression data are clustered. * We have proposed a hybrid model for the extraction of differentially and co-expressed gene expression profiles based on the joint use of an inductive clustering algorithm (SOTA or spectral clustering) and a convolutional neural network. * The proposed hybrid inductive model contributes to increasing objectivity during the formation of the subsets of differentially and co-expressed gene expression profiles to further their applications in various disease diagnosis systems and gene regulatory network reconstruction.