# A Constraints Fusion-induced Symmetric Nonnegative Matrix Factorization Approach for Community Detection

arXiv: https://arxiv.org/abs/2302.12114 · HTML: https://mlsanity.com/paper/2302.12114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 78 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [A Survey of Community Detection Approaches: From Statistical Modeling to Deep Learning](https://mlsanity.com/paper/2101.01669/) (2021)
- [Ultra-Scalable Spectral Clustering and Ensemble Clustering](https://mlsanity.com/paper/1903.01057/) (2019)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Activated Gradients for Deep Neural Networks](https://mlsanity.com/paper/2107.04228/) (2021)
- [A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2301.10499/) (2023)
- [Relational Thematic Clustering with Mutually Preferred Neighbors](https://mlsanity.com/paper/2001.08412/) (2020)

## Abstract (arXiv)

Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF) model is frequently adopted to address this issue owing to its great interpretability and scalability. However, it adopts a single latent factor matrix to represent an undirected network for precisely representing its symmetry, which leads to loss of representation learning ability due to the reduced latent space. Motivated by this discovery, this paper proposes a novel Constraints Fusion-induced Symmetric Nonnegative Matrix Factorization (CFS) model that adopts three-fold ideas: a) Representing a target undirected network with multiple latent factor matrices, thus preserving its representation learning capacity; b) Incorporating a symmetry-regularizer that preserves the symmetry of the learnt low-rank approximation to the adjacency matrix into the loss function, thus making the resultant detector well-aware of the target network's symmetry; and c) Introducing a graph-regularizer that preserves local invariance of the network's intrinsic geometry, thus making the achieved detector well-aware of community structure within the target network. Extensively empirical studies on eight real-world social networks from industrial applications demonstrate that the proposed CFS model significantly outperforms state-of-the-art models in achieving highly-accurate community detection results.