Bayesian Latent Feature Modeling For Modeling Bipartite Networks With Overlapping Groups
Philip Johan Havemann Jørgensen, Technical University of Denmark
Morten Mørup, Technical University of Denmark
Mikkel Nørgaard Schmidt, Technical University of Denmark
Tue Herlau, Technical University of Denmark

Abstract:
Bi-partite networks are commonly modelled using latent class or latent feature models. Whereas the existing latent class models admit marginalization of parameters specifying the strength of interaction between groups, existing latent feature models do not admit analytical marginalization of the param- eters accounting for the interaction strength within the feature representation. We propose a new binary latent feature model that admits analytical marginalization of interaction strengths such that model inference reduces to assigning nodes to latent features. We propose a constraint inspired by the notion of community structure such that the edge density within groups is higher than between groups. Our model further assumes that entities can have different propensities of generating links in one of the modes. The proposed framework is contrasted on both synthetic and real bi-partite networks to the infinite relational model and the infinite Bernoulli mixture model. We find that the model provides a new latent feature represen- tation of structure while in link-prediction performing close to existing models. Our current extension of the notion of communities and collapsed inference to binary latent feature representations in bipartite networks provides a new frame- work for accounting for structure in bi-partite networks using binary latent feature representations providing interpretable representations that well characterize structure as quantified by link prediction.