A Probabilistic Self-Organizing Map for Binary Data Topographic Clustering

This paper introduces a probabilistic self-organizing map for topographic clustering, analysis and visualization of multivariate binary data or categorical data using binary coding. We propose a probabilistic formalism dedicated to binary data in which cells are represented by a Bernoulli distribution. Each cell is characterized by a prototype with the same binary coding as used in the data space and the probability of being different from this prototype. The learning algorithm, BeSOM, that we propose is an application of the EM standard algorithm. We illustrate the power of this method with six data sets taken from a public data set repository. The results show a good quality of the topological ordering and homogenous clustering.