Unsupervised Data Partitioning: a Bayesian Approach

A Bayesian-based methodology is presented which automatically penalises over-complex models being fitted to unknown data. We show that, with a Gaussian mixture model, the approach is able to select an `optimal' number of components in the model and so partition data sets. 1 Introduction For many data sets, methods which perform some form of unsupervised partitioning or modelling are particularly useful. A variety of model (or cluster) validity measures have been proposed and these clearly have their place [3, 7]. The problem of model validation and selection may be solved in a particularly elegant manner, however, if we adopt a Bayesian paradigm. The Bayesian approach may be crudely regarded as estimating the uncertainty of the model as a whole, given the data -- the model `fit' -- and secondly the uncertainty in the estimated parameters themselves. Whilst the first measure decreases with the number of parameters, the second increases as more parameters are estimated using a finite dat..