Two-dimensional contingency or co-occurrence tables arise frequently in important applications such as text, web-log and market-basket data analysis. A basic problem in contingency table analysis is co-clustering: simultaneous clustering of the rows and columns. A novel theoretical formulation views the contingency table as an empirical joint probability distribution of two discrete random variables and poses the co-clustering problem as an optimization problem in information theory---the optimal co-clustering maximizes the mutual information between the clustered random variables subject to constraints on the number of row and column clusters. We present an innovative co-clustering algorithm that monotonically increases the preserved mutual information by intertwining both the row and column clusterings at all stages. Using the practical example of simultaneous word-document clustering, we demonstrate that our algorithm works well in practice, especially in the presence of sparsity and high-dimensionality.

In this paper we propose a new information-theoretic divisive algorithm for word clustering applied to text classification. In previous work, such "distributional clustering" of features has been found to achieve improvements over feature selection in terms of classification accuracy, especially at lower number of features [2, 28]. However the existing clustering techniques are agglomerative in nature and result in (i) sub-optimal word clusters and (ii) high computational cost. In order to explicitly capture the optimality of word clusters in an information theoretic framework, we first derive a global criterion for feature clustering. We then present a fast, divisive algorithm that monotonically decreases this objective function value, thus converging to a local minimum. We show that our algorithm minimizes the "within-cluster Jensen-Shannon divergence" while simultaneously maximizing the "between-cluster Jensen-Shannon divergence". In comparison to the previously proposed agglomerative strategies our divisive algorithm achieves higher classification accuracy especially at lower number of features. We further show that feature clustering is an effective technique for building smaller class models in hierarchical classification. We present detailed experimental results using Naive Bayes and Support Vector Machines on the 20 Newsgroups data set and a 3-level hierarchy of HTML documents collected from Dmoz Open Directory.