A permutation-based algorithm for block clustering |
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Authors: | Diane E Duffy adolfo J Quiroz |
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Institution: | (1) Bellcore, Morristowri, NJ, USA;(2) Universidad Simon Bolivar, Caracas, Venezuela |
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Abstract: | Hartigan (1972) discusses the direct clustering of a matrix of data into homogeneous blocks. He introduces a stepwise divisive
method for block clustering within a certain class of block structures which induce clustering trees for both row and column
margins. While this class of structures is appealing, the stopping criterion for his method, which is based on asymptotic
theory and the assumption that the individual elements of the data matrix are normally distributed, is quite restrictive.
In this paper we propose a permutation-based algorithm for block clustering within the same class of block structures. By
using permutation arguments to decide where to split and when to stop, our algorithm becomes applicable in a wide variety
of cases, including matrices of categorical data and matrices of small-to-moderate size. In addition, our algorithm offers
considerable flexibility in how block homogeneity is defined. The algorithm is studied in a series of simulation experiments
on matrices of known structure, and illustrated in examples drawn from the fields of taxonomy, political science, and data
architecture. |
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Keywords: | Binary splitting Blck clustering Markov chain simulation method Permutation distribution |
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