# Directed mixed membership stochastic blockmodel

arXiv: https://arxiv.org/abs/2101.02307 · HTML: https://mlsanity.com/paper/2101.02307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 17 of 17)

- [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)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [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)
- [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)
- [Overlapping Clustering Models, and One (class) SVM to Bind Them All](https://mlsanity.com/paper/1806.06945/) (2018)
- [Optimal Bipartite Network Clustering](https://mlsanity.com/paper/1803.06031/) (2018)
- [Randomized spectral co-clustering for large-scale directed networks](https://mlsanity.com/paper/2004.12164/) (2020)
- [Matched bipartite block model with covariates](https://mlsanity.com/paper/1703.04943/) (2017)

## Built on by (most cited first, 2 of 2)

- [Bipartite mixed membership distribution-free model. A novel model for community detection in overlapping bipartite weighted networks](https://mlsanity.com/paper/2211.00912/) (2022)
- [Overlapping and nonoverlapping models](https://mlsanity.com/paper/2111.01392/) (2021)

## Abstract (arXiv)

Mixed membership modeling for undirected networks has been extensively explored in network science over the past few years. Despite the substantial progress made for undirected cases, handling mixed membership structures in directed networks continues to pose substantial difficulties. To address this gap, we introduce the Directed Mixed Membership Stochastic Blockmodel (DiMMSB), a novel framework tailored for directed networks with overlapping communities. A key feature of DiMMSB is its ability to treat the row and column nodes of the adjacency matrix as distinct entities, each potentially following its own community organization. Building on this model, we develop DiSP, an efficient spectral procedure to estimate mixed memberships for both sets of nodes. Through delicate analysis, we derive node-specific error bounds of DiSP under mild sparsity conditions. Simulation results support the theoretical results, demonstrating that DiSP achieves lower error rates and faster computation than its competitor. Moreover, applications to real data highlight DiSP's effectiveness in uncovering asymmetric structural patterns.