## 1 Introduction  
The modern artificial information processing systems used in various fields of intelligent data analysis and machine learning are mostly based on an analogy with the functioning of corresponding processes in biological organisms. Such processes include the functioning of gene networks, immune processes, the functioning of neural networks, and so on. The peculiarity of such systems is their high level of complexity, ability to learn, parallel processing of information, high level of security, and ability to recognize and make appropriate decisions. In this context, the development of modern artificial models for processing big data is possible with the use of a systemic approach, which involves the comprehensive application of knowledge and methods from various practical fields, such as molecular biology, mathematics, computer science, physics, and chemistry. Suchapproaches create conditions for increasing the objectivity of processing big data in real time, through the use of ensembles of methods, hybrid models, and effective quality criteria for assessing results at the corresponding stage of information processing implementation. One of the current problems in modern bioinformatics is the processing of the gene expression data obtained in DNA microchip experiments [1] or the more modern method of mRNA molecule sequencing [2]. The peculiarities of experimental data include a large number of genes that determine the state of the corresponding biological organism. As is well known, the number of expressed (active) genes that make up the human genome is approximately 25,000. At the same time, the number of each type of gene varies in the range from zero to hundreds of thousands. Creating medical diagnostic systems or models of gene regulatory networks using full data is not effective, because the process of interpreting the obtained results, in this case, is problematic. Currently, deep learning models are actively used to process large datasets, such as deep neural networks [3], convolutional neural networks [4], and artificial deep networks [5], which allow achieving a satisfactory diagnostic accuracy on large data, but at the same time, there are problems regarding the training time, network sensitivity, and verification of obtained models on other similar data. Solutions to the aforementioned problems are possible through the development and improvement of existing methods, models, and algorithms for processing large datasets. The implementation of this process involves the formation of quality experimental data by applying appropriate methods for normalizing gene expression values and reducing low-expressed genes in the first stage. The second stage involves the problem of forming subsets of differentially expressed and mutually correlated expression profiles of genes using hybrid models of high-dimensional data clustering. The third stage involves the development of a disease diagnostic model based on the formed clusters of gene expression profiles using deep learning methods, with corresponding verification of the obtained results. This manuscript extends the authors' previous work on gene expression data preprocessing [6], comparative analysis of gene expression profile proximity metrics [7], noninformative gene removal using statistical criteria and Shannon entropy [8], and the formation of subsets of mutually correlated and differently expressed gene expression profiles through the joint application of various clustering and classification techniques [9]. This manuscript presents the following main contributions:  
* We introduce an inductive model of objective clustering, which utilizes a spectral clustering algorithm to generate subsets of gene expression profiles that are differentially expressed and mutually correlated. * We propose and practically implement a hybrid model for diagnosing various types of cancer, which combines the inductive spectral clustering algorithm, the random forest classifier, a convolutional neural network, and the alternative voting method.