Some Fuzzy Clustering Algorithms for Mixed Numerical and Categorical Data based on Fuzzy k-Modes and Fuzzy k-partitions

Abstract

For fuzzy clustering for numerical data, not only Bezdek-type fuzzification but also entropy-regularization and q-divergence-regularization are adopted. Furthermore, cluster size controller was introduced. For fuzzy clustering for mixed numerical and categorical data, only Bezdek-type fuzzification is adopted based on fuzzy k-modes for categorical data, and cluster size controller was not introduced. In this report, six algorithms are proposed as variants of fuzzy clustering for mixed numerical and categorical data, where all the proposed algorithms introduce cluster size controller, three of these are based on fuzzy k-modes for categorical data, and the other three are based on fuzzy k-partitions for categorical data. Through numerical experiments using an artificial dataset, properties of proposed algorithms are observed.