SMLSOM: The shrinking maximum likelihood self-organizing map

Abstract

Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model selection. This paper proposes an efficient algorithm that automatically selects a suitable number of clusters based on a probability distribution model framework. The algorithm includes the following two components. First, a generalization of Kohonen's self-organizing map (SOM) is introduced. In Kohonen's SOM, clusters are modeled as mean vectors. In the generalized SOM, each cluster is modeled as a probabilistic distribution and constructed by samples classified based on the likelihood. Second, the dynamically updating method of the SOM structure is introduced. In Kohonen's SOM, each cluster is tied to a node of a fixed two-dimensional lattice space and learned using neighborhood relations between nodes based on Euclidean distance. The extended SOM defines a graph with clusters as vertices and neighborhood relations as links and updates the graph structure by cutting weakly connected and unnecessary vertex deletions. The weakness of a link is measured using the Kullback–Leibler divergence, and the redundancy of a vertex is measured using the minimum description length. Those extensions make it efficient to determine the appropriate number of clusters. Compared with existing methods, the proposed method is computationally efficient and can accurately select the number of clusters.