Model-based co-clustering for mixed type data

The importance of clustering for creating groups of observations is well known. The emergence of high-dimensional data sets with a huge number of features leads to co-clustering techniques, and several methods have been developed for simultaneously producing groups of observations and features. By grouping the data set into blocks (the crossing of a row-cluster and a column-cluster), these techniques can sometimes better summarize the data set and its inherent structure. The Latent Block Model (LBM) is a well-known method for performing co-clustering. However, recently, contexts with features of different types (here called mixed type data sets) are becoming more common. The LBM is not directly applicable to this kind of data set. Here a natural extension of the usual LBM to the “Multiple Latent Block Model” (MLBM) is proposed in order to handle mixed type data sets. Inference is performed using a Stochastic EM-algorithm that embeds a Gibbs sampler, and allows for missing data situations. A model selection criterion is defined to choose the number of row and column clusters. The method is then applied to both simulated and real data sets.