Co-Clustering Multi-View Data Using the Latent Block Model

The Latent Block Model (LBM) is a prominent model-based co-clustering method,returning parametric representations of each block cluster and allowing the useof well-grounded model selection methods. The LBM, while adapted in literatureto handle different feature types, cannot be applied to datasets consisting ofmultiple disjoint sets of features, termed views, for a common set ofobservations. In this work, we introduce the multi-view LBM, extending the LBMmethod to multi-view data, where each view marginally follows an LBM. In thecase of two views, the dependence between them is captured by a clustermembership matrix, and we aim to learn the structure of this matrix. We developa likelihood-based approach in which parameter estimation uses a stochastic EMalgorithm integrating a Gibbs sampler, and an ICL criterion is derived todetermine the number of row and column clusters in each view. To motivate theapplication of multi-view methods, we extend recent work developing hypothesistests for the null hypothesis that clusters of observations in each view areindependent of each other. The testing procedure is integrated into the modelestimation strategy. Furthermore, we introduce a penalty scheme to generatesparse row clusterings. We verify the performance of the developed algorithmusing synthetic datasets, and provide guidance for optimal parameter selection.Finally, the multi-view co-clustering method is applied to a complex genomicsdataset, and is shown to provide new insights for high-dimension multi-viewproblems.