Cluster Partitions Optimization Using the Latent Class Analysis Technique

Abstract

The paper explores the formation of a cluster partition using a system of bundles of vectors. Each object is represented by a vector with coordinates corresponding to its characteristic factors. The study focuses on the principles of changes in the total density of these bundles when objects move from one cluster to another. Based on the findings, an algorithm is proposed to reduce the total intracluster variance of the initial cluster partition.
 The proposed algorithm is based on a modern technique for analyzing latent classes. This technique emphasizes that the forming factors of objects within each cluster should be highly correlated. Since the number of forming factors is arbitrary, the algorithm replaces this requirement with the maximum possible proximity of object factor vectors to the average vector within each cluster. The degree of this closeness is referred to as the tightness of the cluster vector bundle.
 The paper also introduces a new method for quantifying clusters in the improvable clustering constructed using the proposed algorithm. A practical example of the algorithm's application to process medical data is presented. The study discusses the reasons for the dependence of the algorithm's outcome on the choice of initial cluster partition.