# Mixed membership distribution-free model

arXiv: https://arxiv.org/abs/2112.04389 · HTML: https://mlsanity.com/paper/2112.04389/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 98 references that are in the map.
- First posted on arXiv 4 Dec 2021.

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

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (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)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [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)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [Achieving Exact Cluster Recovery Threshold via Semidefinite Programming](https://mlsanity.com/paper/1412.6156/) (2014)
- [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)
- [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)
- [The Slashdot Zoo: Mining a Social Network with Negative Edges](https://mlsanity.com/paper/1710.11395/) (2017)
- [Overlapping Clustering Models, and One (class) SVM to Bind Them All](https://mlsanity.com/paper/1806.06945/) (2018)
- [Estimating the number of communities in networks by spectral methods](https://mlsanity.com/paper/1507.00827/) (2015)
- [Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence](https://mlsanity.com/paper/1509.06418/) (2015)
- [Randomized Spectral Clustering in Large-Scale Stochastic Block Models](https://mlsanity.com/paper/2002.00839/) (2020)
- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [Significance-based community detection in weighted networks](https://mlsanity.com/paper/1601.05630/) (2016)
- [A useful criterion on studying consistent estimation in community detection](https://mlsanity.com/paper/2109.14950/) (2021)
- [Distribution-Free Model for Community Detection](https://mlsanity.com/paper/2111.07495/) (2021)
- [Degree-corrected distribution-free model for community detection in weighted networks](https://mlsanity.com/paper/2111.10553/) (2021)

## 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)
- [Mixed membership estimation for categorical data with weighted responses](https://mlsanity.com/paper/2310.10989/) (2023)

## Abstract (arXiv)

We consider the problem of community detection in overlapping weighted networks, where nodes can belong to multiple communities and edge weights can be finite real numbers. To model such complex networks, we propose a general framework - the mixed membership distribution-free (MMDF) model. MMDF has no distribution constraints of edge weights and can be viewed as generalizations of some previous models, including the well-known mixed membership stochastic blockmodels. Especially, overlapping signed networks with latent community structures can also be generated from our model. We use an efficient spectral algorithm with a theoretical guarantee of convergence rate to estimate community memberships under the model. We also propose the fuzzy weighted modularity to evaluate the quality of community detection for overlapping weighted networks with positive and negative edge weights. We then provide a method to determine the number of communities for weighted networks by taking advantage of our fuzzy weighted modularity. Numerical simulations and real data applications are carried out to demonstrate the usefulness of our mixed membership distribution-free model and our fuzzy weighted modularity.