Clustering as average entropy minimization and its application to structure analysis of complex systems

A clustering procedure is discussed from the point of view of minimum average entropy, and examined as a possible approach to structure analysis of a system consisting of some partial subsystems. Most practical algorithms to carry out clustering tasks are based on the notion of distance between two objects. For the purpose of taking ´more-than-two-elements correlation´ into account, the article formulates a clustering procedure as a process of average entropy minimization within a formal framework where each object is characterized by a set of predicates or attributes as a binary vector, and discusses its significance in structure analysis. Examples show that the proposed approach is indeed capable of identifying constituent components of structured complex systems, and revealing subtle multilateral properties among groups of objects