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Article Dans Une Revue Advances in Data Analysis and Classification Année : 2018

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

Résumé

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.
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Dates et versions

hal-03780733 , version 1 (19-09-2022)

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Citer

Gérard Govaert, Mohamed Nadif. Mutual information, phi-squared and model-based co-clustering for contingency tables. Advances in Data Analysis and Classification, 2018, 12 (3), pp.455-488. ⟨10.1007/s11634-016-0274-6⟩. ⟨hal-03780733⟩
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