A finite mixture approach for biclustering bipartite networks.

Bipartite networks are particularly useful for representing relationships between disjoint sets of nodes, called sending and receiving nodes. The mixtures of latent trait analyzers are modified to achieve a twofold objective with regard to bipartite networks: i) performing joint clustering of sending and receiving nodes; ii) using a latent trait to model the dependence between receiving nodes. Therefore, the suggested model cannot only partition the data matrix into homogeneous blocks, as in the biclustering approach, but also capture the latent variability of network connections within each block, as in the latent trait framework. The proposal also admits the inclusion of nodal attributes on the latent layer of the model, in order to understand how these influence cluster formation. An EM algorithm with a variational approximation is proposed to estimate the model parameters. The performance of the model is evaluated through a simulation study with a different number of nodes and partitions.