Bayesian Solutions to the Label Switching Problem

Authors:
Kai Puolamäki;Samuel Kaski
Affiliations:
Helsinki Institute for Information Technology HIIT Department of Information and Computer Science, Helsinki University of Technology, Finland FI-02015;Helsinki Institute for Information Technology HIIT Department of Information and Computer Science, Helsinki University of Technology, Finland FI-02015
Venue:
IDA '09 Proceedings of the 8th International Symposium on Intelligent Data Analysis: Advances in Intelligent Data Analysis VIII
Year:
2009

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Abstract

The label switching problem, the unidentifiability of the permutation of clusters or more generally latent variables, makes interpretation of results computed with MCMC sampling difficult. We introduce a fully Bayesian treatment of the permutations which performs better than alternatives. The method can even be used to compute summaries of the posterior samples for nonparametric Bayesian methods, for which no good solutions exist so far. Although being approximative in that case, the results are very promising. The summaries are intuitively appealing: A summarized cluster is defined as a set of points for which the likelihood of being in the same cluster is maximized.