Sociedad de Estadfstica e Investigaci6n Operativa Test (1997) Vol. 6, No. 2, pp. 397-416 A fast permutation-based algorithm for block clustering I. Llatas CESMa ~ Departamento de Procesos y Sistemas Universidad Sim6n Bolfvar, Caracas, Venezuela A.J. Quiroz Departamento de Cdmputo Cientffico y Estadfstica Universidad Sim6n Bolfvar, Caracas, Venezuela J.M. Renrm Departamento de Matemdticas, Apartado Postal 89000 Universidad Simdn Bolfvar, Caracas, Venezuela Abstract A stepwise divisive procedure for the clustering of numerical data recorded in ma- trix form into homogeneous groups is introduced. The methodology relates to those proposed by Hartigan (1972) and Duffy and Quiroz (1991). As the latter, the pro- posed 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. Key Words: Binary splitting, Bayesian sequential analysis AMS subject classification: block clustering, permutation distribution, 1 Introduction When numerical data are recorded in matrix form, useful information on how the row and column variables explain the data, can be obtained by reordering the rows and columns, and performing a clustering of the ma- trix into homogeneous rectangular blocks. Methodology for performing this type of clustering (block clustering or direct clustering) has been discussed in Hartigan (1972, 1975) and in Duffy and Quiroz (1991), where exam- ples of their application are given. Hartigan proposes a stepwise divisive Received: November 1995; Accepted: October 1996