A Novel Approach for Biclustering Bipartite Networks: An Extension of Finite Mixtures of Latent Trait Analyzers

In the context of network data, bipartite networks are of particular interest, as they provide a useful description of systems representing relationships between sending and receiving nodes. In this framework, we extend the mixture of latent trait analyzers (MLTA) model with concomitant variables (nodal attributes) to perform a joint clustering of the two disjoint sets of nodes of a bipartite network, as in the biclustering framework. In detail, sending nodes are partitioned into clusters (called components) via a finite mixture of latent trait models. In each component, receiving nodes are partitioned into clusters (called segments) by adopting a flexible and parsimonious specification of the linear predictor. Residual dependence between receiving nodes is modeled via a multidimensional latent trait, as in the original MLTA specification. Furthermore, by incorporating nodal attributes into the model’s latent layer, we gain insight into how these attributes impact the formation of components. To estimate model parameters, an EM-type algorithm based on a Gauss-Hermite approximation of intractable integrals is proposed. A simulation study is conducted to test the performance of the model in terms of clustering and parameters’ recovery. The proposed model is applied to a bipartite network on pediatric patients possibly affected by appendicitis with the objective of identifying groups of patients (sending nodes) being similar with respect to subsets of clinical conditions (receiving nodes).