Co-clustering is a class of unsupervised data analysis techniques that extract the existing underlying dependency structure between the instances and variables of a data table as homogeneous blocks. Most of those techniques are limited to variables of the same type. In this paper, we propose a mixed data co-clustering method based on a two-step methodology. In the first step, all the variables are binarized according to a number of bins chosen by the analyst, by equal frequency discretization in the numerical case, or keeping the most frequent values in the categorical case. The second step applies a co-clustering to the instances and the binary variables, leading to groups of instances and groups of variable parts. We apply this methodology on several data sets and compare with the results of a Multiple Correspondence Analysis applied to the same data.

The goal of co-clustering is to jointly perform a clustering of rows and a clustering of columns of a data table. Proposed by [Good, 1965] then by [Hartigan, 1975], co-clustering is an extension of the standard clustering that extracts the underlying structure in the data in the form of clusters of row and clusters of columns. The advantage of this technique, over the standard clustering, lies in the joint (simultaneous) analysis of the rows and columns which enables extracting the maximum of information about the interdependence between the two entities. The utility of co-clustering lies in its capacity to create easily interpretable clusters and its capability to reduce a large data table into a significantly smaller matrix having the same structure as the orig-Aichetou Bouchareb, Marc Boullé and Fabrice Clérot: Orange Labs, 2 Avenue Pierre Marzin 22300 Lannion - France, e-mail: firstname.

We propose a MAP Bayesian approach to perform and evaluate a co-clustering of mixed-type data tables. The proposed model infers an optimal segmentation of all variables then performs a co-clustering by minimizing a Bayesian model selection cost function. One advantage of this approach is that it is user parameter-free. Another main advantage is the proposed criterion which gives an exact measure of the model quality, measured by probability of fitting it to the data. Continuous optimization of this criterion ensures finding better and better models while avoiding data over-fitting. The experiments conducted on real data show the interest of this co-clustering approach in exploratory data analysis of large data sets.