Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks

TL;DR

This paper introduces the Bipartite Mixed Membership Distribution-Free (BiMMDF) model, a flexible approach for community detection in overlapping bipartite weighted networks that generalizes previous models and handles various distributions.

Contribution

The paper proposes the BiMMDF model, extending mixed membership models to bipartite weighted networks with distribution-free assumptions and provides an efficient, consistent estimation algorithm.

Findings

BiMMDF effectively models overlapping bipartite signed networks.

The model demonstrates strong performance on synthetic and real-world networks.

Separation conditions for different distributions are established.

Abstract

Modeling and estimating mixed memberships for overlapping unipartite un-weighted networks has been well studied in recent years. However, to our knowledge, there is no model for a more general case, the overlapping bipartite weighted networks. To close this gap, we introduce a novel model, the Bipartite Mixed Membership Distribution-Free (BiMMDF) model. Our model allows an adjacency matrix to follow any distribution as long as its expectation has a block structure related to node membership. In particular, BiMMDF can model overlapping bipartite signed networks and it is an extension of many previous models, including the popular mixed membership stochastic blcokmodels. An efficient algorithm with a theoretical guarantee of consistent estimation is applied to fit BiMMDF. We then obtain the separation conditions of BiMMDF for different distributions. Furthermore, we also consider missing edges for sparse networks. The advantage of BiMMDF is demonstrated in extensive synthetic networks and eight real-world networks.