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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, Bernoulli on self-organizing map, 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.

Results of Norwegian Elite Division soccer games are studied for the year 2003. Previous writers have modelled the number of goals a given team scores in a game and then moved on to evaluating the probabilities of a win, a tie and a loss. However in this work the probabilities of win, tie and loss are modelled directly. There are attempts to improve the fit by including various explanatories.