A.N. Golovenkov1

1 Federal State Autonomous Educational Institution of Higher Education «Saint Petersburg State University of Aerospace Instrumentation» (St. Petersburg, Russia)

1 aleksandr.golovenkov@mail.ru

Problem Statement. Markov chains are of interest across a wide range of applications and domains, such as telecommunications systems, remanufacturing and inventory systems, speech recognition, and more. In recent years, various models have been proposed using Markov chains for predicting multiple categorical data sequences, enabling the discovery of patterns in them. Objective: Conduct an analysis of the application of k-order Markov chains to categorical data analysis. Results: This paper presents a description of a mixed hidden Markov model that offers a solution to the problem of clustering uncertainty. In this model, instead of assigning individuals to c lusters, all data is used to estimate a mixture of hidden Markov models, where each individual belongs to each cluster with a certain probability. Special attention is given to a model adjustment me thod based on the Baum-Welch algorithm, which, together with a selection scheme, allows the use of partial labels in the data to improve the training of hidden Markov models. Practical Relevance. A model tuning method based on the Baum -Welch algorithm is presented. Together with a model selection scheme, this met hod enables the use of partial labels in data to improve the training of hidden Markov models. Further research would benefit from testing this approach to data and sequence analysis using Markov chains.

Golovenkov A.N. Application of k -order Markov chains to categorical data analysis. Dynamics of complex systems. 2026. V. 20. № 2. P. 55−63. DOI: 10.18127/j19997493-202602-06 (in Russian).

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