Mutual information, phi-squared and model-based co-clustering for contingency tables

Gérard Govaert () and Mohamed Nadif ()
Additional contact information
Gérard Govaert: U.M.R. C.N.R.S.
Mohamed Nadif: University of Paris Descartes

Advances in Data Analysis and Classification, 2018, vol. 12, issue 3, No 2, 455-488

Abstract: Abstract Many of the datasets encountered in statistics are two-dimensional in nature and can be represented by a matrix. Classical clustering procedures seek to construct separately an optimal partition of rows or, sometimes, of columns. In contrast, co-clustering methods cluster the rows and the columns simultaneously and organize the data into homogeneous blocks (after suitable permutations). Methods of this kind have practical importance in a wide variety of applications such as document clustering, where data are typically organized in two-way contingency tables. Our goal is to offer coherent frameworks for understanding some existing criteria and algorithms for co-clustering contingency tables, and to propose new ones. We look at two different frameworks for the problem of co-clustering. The first involves minimizing an objective function based on measures of association and in particular on phi-squared and mutual information. The second uses a model-based co-clustering approach, and we consider two models: the block model and the latent block model. We establish connections between different approaches, criteria and algorithms, and we highlight a number of implicit assumptions in some commonly used algorithms. Our contribution is illustrated by numerical experiments on simulated and real-case datasets that show the relevance of the presented methods in the document clustering field.

Keywords: Co-clustering; Biclustering; Contingency table; Information theory; 62-07 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11634-016-0274-6

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