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

arXiv: https://arxiv.org/abs/2211.00912 · HTML: https://mlsanity.com/paper/2211.00912/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 121 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 30 of 37)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Exact Recovery in the Stochastic Block Model](https://mlsanity.com/paper/1405.3267/) (2014)
- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Clustering and Community Detection in Directed Networks: A Survey](https://mlsanity.com/paper/1308.0971/) (2013)
- [A Survey of Signed Network Mining in Social Media](https://mlsanity.com/paper/1511.07569/) (2015)
- [Impact of regularization on Spectral Clustering](https://mlsanity.com/paper/1312.1733/) (2013)
- [Learning Latent Block Structure in Weighted Networks](https://mlsanity.com/paper/1404.0431/) (2014)
- [20 years of network community detection](https://mlsanity.com/paper/2208.00111/) (2022)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Detecting Overlapping Communities in Networks Using Spectral Methods](https://mlsanity.com/paper/1412.3432/) (2014)
- [Estimating Mixed Memberships with Sharp Eigenvector Deviations](https://mlsanity.com/paper/1709.00407/) (2017)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Analysis of spectral clustering algorithms for community detection: the general bipartite setting](https://mlsanity.com/paper/1803.04547/) (2018)
- [Hypergraph Spectral Clustering in the Weighted Stochastic Block Model](https://mlsanity.com/paper/1805.08956/) (2018)
- [Spectral Algorithms for Community Detection in Directed Networks](https://mlsanity.com/paper/2008.03820/) (2020)
- [Convexified Modularity Maximization for Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1512.08425/) (2015)
- [On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations](https://mlsanity.com/paper/1607.00084/) (2016)
- [Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/1310.2273/) (2013)
- [Achieving Exact Cluster Recovery Threshold via Semidefinite Programming: Extensions](https://mlsanity.com/paper/1502.07738/) (2015)
- [Co-citation and Co-authorship Networks of Statisticians](https://mlsanity.com/paper/2204.11194/) (2022)
- [Overlapping Clustering Models, and One (class) SVM to Bind Them All](https://mlsanity.com/paper/1806.06945/) (2018)
- [Randomized Spectral Clustering in Large-Scale Stochastic Block Models](https://mlsanity.com/paper/2002.00839/) (2020)
- [Optimal Bipartite Network Clustering](https://mlsanity.com/paper/1803.06031/) (2018)
- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [Peeling Bipartite Networks for Dense Subgraph Discovery](https://mlsanity.com/paper/1611.02756/) (2016)
- [Significance-based community detection in weighted networks](https://mlsanity.com/paper/1601.05630/) (2016)

## Built on by (most cited first, 4 of 4)

- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (2024)
- [Mixed membership estimation for categorical data with weighted responses](https://mlsanity.com/paper/2310.10989/) (2023)
- [Multilayer Artificial Benchmark for Community Detection (mABCD)](https://mlsanity.com/paper/2507.10795/) (2025)
- [Estimating mixed memberships in multi-layer networks](https://mlsanity.com/paper/2404.03916/) (2024)

## Abstract (arXiv)

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.