# Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization

arXiv: https://arxiv.org/abs/2205.00626 · HTML: https://mlsanity.com/paper/2205.00626/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 76 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 25 of 25)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition](https://mlsanity.com/paper/2002.04457/) (2020)
- [Spectral and matrix factorization methods for consistent community detection in multi-layer networks](https://mlsanity.com/paper/1704.07353/) (2017)
- [Community Detection in Multiplex Networks](https://mlsanity.com/paper/1910.07646/) (2019)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds](https://mlsanity.com/paper/1303.2221/) (2013)
- [Community Detection via Maximization of Modularity and Its Variants](https://mlsanity.com/paper/1507.00787/) (2015)
- [Clustering Network Layers With the Strata Multilayer Stochastic Block Model](https://mlsanity.com/paper/1507.01826/) (2015)
- [Combinatorial Analysis of Multiple Networks](https://mlsanity.com/paper/1303.4986/) (2013)
- [Clustering by Orthogonal NMF Model and Non-Convex Penalty Optimization](https://mlsanity.com/paper/1906.00570/) (2019)
- [Spectral Clustering for Multiple Sparse Networks: I](https://mlsanity.com/paper/1805.10594/) (2018)
- [Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms](https://mlsanity.com/paper/1708.02620/) (2017)
- [Latent heterogeneous multilayer community detection](https://mlsanity.com/paper/1806.07963/) (2018)
- [MuxViz: A Tool for Multilayer Analysis and Visualization of Networks](https://mlsanity.com/paper/1405.0843/) (2014)
- [ABACUS: frequent pAttern mining-BAsed Community discovery in mUltidimensional networkS](https://mlsanity.com/paper/1303.2025/) (2013)
- [A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks](https://mlsanity.com/paper/1608.06196/) (2016)
- [Non-Negative Matrix Factorizations for Multiplex Network Analysis](https://mlsanity.com/paper/1612.00750/) (2016)
- [Relating modularity maximization and stochastic block models in multilayer networks](https://mlsanity.com/paper/1804.01964/) (2018)
- [Structural and Functional Discovery in Dynamic Networks with Non-negative Matrix Factorization](https://mlsanity.com/paper/1305.7169/) (2013)
- [Structure of Triadic Relations in Multiplex Networks](https://mlsanity.com/paper/1307.6780/) (2013)
- [Clustering multilayer graphs with missing nodes](https://mlsanity.com/paper/2103.03235/) (2021)
- [Community detection in multiplex networks using locally adaptive random walks](https://mlsanity.com/paper/1507.01890/) (2015)
- [Super-resolution community detection for layer-aggregated multilayer networks](https://mlsanity.com/paper/1609.04376/) (2016)

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

- [Discriminative community detection for multiplex networks](https://mlsanity.com/paper/2410.00724/) (2024)
- [Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection](https://mlsanity.com/paper/2610.01361/) (2026)

## Abstract (arXiv)

Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different ways necessitating the use of multiplex networks where multiple links are used to model the interactions. One of the major tools for inferring network topology is community detection. Although there are numerous works on community detection in single-layer networks, existing community detection methods for multiplex networks mostly learn a common community structure across layers and do not take the heterogeneity across layers into account. In this paper, we introduce a new multiplex community detection method that identifies communities that are common across layers as well as those that are unique to each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix Tri-Factorization, represents the adjacency matrix of each layer as the sum of two low-rank matrix factorizations corresponding to the common and private communities, respectively. Unlike most of the existing methods, which require the number of communities to be pre-determined, the proposed method also introduces a two stage method to determine the number of common and private communities. The proposed algorithm is evaluated on synthetic and real multiplex networks, as well as for multiview clustering applications, and compared to state-of-the-art techniques.