# Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection

arXiv: https://arxiv.org/abs/2610.01361 · HTML: https://mlsanity.com/paper/2610.01361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 19 of 19)

- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Ultra-Scalable Spectral Clustering and Ensemble Clustering](https://mlsanity.com/paper/1903.01057/) (2019)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [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)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Contact patterns among high school students](https://mlsanity.com/paper/1409.5318/) (2014)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels](https://mlsanity.com/paper/2212.05053/) (2022)
- [Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms](https://mlsanity.com/paper/1708.02620/) (2017)
- [Towards effective visual analytics on multiplex and multilayer networks](https://mlsanity.com/paper/1501.01666/) (2015)
- [Latent heterogeneous multilayer community detection](https://mlsanity.com/paper/1806.07963/) (2018)
- [ABACUS: frequent pAttern mining-BAsed Community discovery in mUltidimensional networkS](https://mlsanity.com/paper/1303.2025/) (2013)
- [Non-Negative Matrix Factorizations for Multiplex Network Analysis](https://mlsanity.com/paper/1612.00750/) (2016)
- [Clustering multilayer graphs with missing nodes](https://mlsanity.com/paper/2103.03235/) (2021)
- [Community detection in multiplex networks based on orthogonal nonnegative matrix tri-factorization](https://mlsanity.com/paper/2205.00626/) (2022)
- [Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model](https://mlsanity.com/paper/2601.06262/) (2026)
- [On solving symmetric multi-type orthogonal non-negative matrix tri-factorization problem](https://mlsanity.com/paper/2606.08291/) (2026)

## Abstract (arXiv)

Multilayer networks allow the modeling of interactions between the same entities across different contexts, such as temporal observations, varying settings, or interactions of different types. The goal of community detection in multilayer networks is to identify groups of nodes exhibiting similar connectivity patterns, which may vary across layers. We propose a method based on a joint nonnegative symmetric matrix trifactorization for community detection in multilayer networks, where each graph is approximated by a nonnegative symmetric matrix trifactorization. Our approach enforces constraints on the factor matrices so that communities are disjoint and shared across layers, while allowing each layer to have its own connectivity patterns and node degrees. This flexibility enables the model to capture both local and global structural variations across layers. We also develop an algorithm to efficiently solve this problem. We evaluate multilayer community detection methods using the multilayer degree-corrected stochastic block model (MDCBM), a flexible framework for generating realistic multilayer graphs with heterogeneous degrees and varying connectivity patterns. Experiments show that our method reliably detects communities across diverse regimes, whereas existing state-of-the-art approaches are often limited by restrictive structural assumptions.