A fast permutation-based algorithm for block clustering

A stepwise divisive procedure for the clustering of numerical data recorded in matrix form into homogeneous groups is introduced. The methodology relates to those proposed by Hartigan (1972) and Duffy and Quiroz (1991). As the latter, the proposed methodology uses the permutation distribution of the data in a block as the reference distribution to make inferences about the presence of clustering structure. A local (within block) criteria and Bayesian sequential decision methodology are used to evaluate the significance of potential partitions of blocks, resulting in an algorithm which is faster than those considered by Duffy and Quiroz (1991). The class of possible clustering structures that our procedure can discover is also larger than those previously considered in the literature.