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There are two notoriously hard problems in cluster analysis, estimating thenumber of clusters, and checking whether the population to be clustered is notactually homogeneous. Given a dataset, a clustering method and a clustervalidation index, this paper proposes to set up null models that capturestructural features of the data that cannot be interpreted as indicatingclustering. Artificial datasets are sampled from the null model with parametersestimated from the original dataset. This can be used for testing the nullhypothesis of a homogeneous population against a clustering alternative. It canalso be used to calibrate the validation index for estimating the number ofclusters, by taking into account the expected distribution of the index underthe null model for any given number of clusters. The approach is illustrated bythree examples, involving various different clustering techniques (partitioningaround medoids, hierarchical methods, a Gaussian mixture model), validationindexes (average silhouette width, prediction strength and BIC), and issuessuch as mixed type data, temporal and spatial autocorrelation.

Flexible parametric bootstrap for testing homogeneity against clustering and assessing the number of clusters