Clustering Using Monte Carlo Cross-Validation

Padhraic Smyth

Finding the "right" number of clusters, k, for a data set is a difficult, and often ill-posed, problem. In a probabilistic clustering context, likelihood-ratios, penalized likelihoods, and Bayesian techniques are among the more popular techniques. In this paper a new cross-validated likelihood criterion is investigated for determining cluster structure. A practical clustering algorithm based on Monte Carlo cross-validation (MCCV) is introduced. The algorithm permits the data analyst to judge if there is strong evidence for a particular k, or perhaps weaker evidence over a sub-range of k values. Experimental results with Gaussian mixtures on real and simulated data suggest that MCCV provides genuine insight into cluster structure. v-fold cross-validation appears inferior to the penalized likelihood method (BIC), a Bayesian algorithm (AutoClass v2.0), and the new MCCV algorithm. Overall, MCCV and AutoClass appear the most reliable of the methods. MCCV provides the data-miner with a useful data-driven clustering tool which complements the fully Bayesian approach.

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