Co-clustering model for three-way data
Résumé
Three-way data can be seen as a collection of two-way matrices, as we can meet when the same samples are measured several times in different conditions.
Considering such data as a matrix in which each element is the observation of a random function, we propose a new co-clustering methodology which aims to produce simultaneously a clustering of the rows and a clustering of the columns. The proposed functional latent block model (funLBM) extends the usual latent block model to the functional case by assuming that the curves of one block live into a low-dimensional functional subspace. Thus, funLBM is able to model and cluster large data set with high-frequency curves. An stochastic EM algorithm embedding a Gibbs sampler is proposed for model inference. An ICL model selection criterion is also derived to address the problem of choosing the number of row and column clusters. Numerical experiments on simulated data and application on electricity consumptions show the usefulness of the proposed methodology.