# High-order Order Proximity-Incorporated, Symmetry and Graph-Regularized Nonnegative Matrix Factorization for Community Detection

arXiv: https://arxiv.org/abs/2203.03876 · HTML: https://mlsanity.com/paper/2203.03876/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 43 references that are in the map.
- First posted on arXiv 8 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [Producing a Unified Graph Representation from Multiple Social Network Views](https://mlsanity.com/paper/1301.5809/) (2013)

## Built on by (most cited first, 1 of 1)

- [Concept Factorization via Self-Representation and Adaptive Graph Structure Learning](https://mlsanity.com/paper/2505.03390/) (2025)

## Abstract (arXiv)

Community describes the functional mechanism of a network, making community detection serve as a fundamental graph tool for various real applications like discovery of social circle. To date, a Symmetric and Non-negative Matrix Factorization (SNMF) model has been frequently adopted to address this issue owing to its high interpretability and scalability. However, most existing SNMF-based community detection methods neglect the high-order connection patterns in a network. Motivated by this discovery, in this paper, we propose a High-Order Proximity (HOP)-incorporated, Symmetry and Graph-regularized NMF (HSGN) model that adopts the following three-fold ideas: a) adopting a weighted pointwise mutual information (PMI)-based approach to measure the HOP indices among nodes in a network; b) leveraging an iterative reconstruction scheme to encode the captured HOP into the network; and c) introducing a symmetry and graph-regularized NMF algorithm to detect communities accurately. Extensive empirical studies on eight real-world networks demonstrate that an HSGN-based community detector significantly outperforms both benchmark and state-of-the-art community detectors in providing highly-accurate community detection results.