# Self-supervised Symmetric Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/2103.01689 · HTML: https://mlsanity.com/paper/2103.01689/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 9 of 9)

- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Locally Weighted Ensemble Clustering](https://mlsanity.com/paper/1605.05011/) (2016)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF](https://mlsanity.com/paper/1907.02404/) (2019)
- [Convex Sparse Spectral Clustering: Single-view to Multi-view](https://mlsanity.com/paper/1511.06860/) (2015)
- [Inexact Block Coordinate Descent Methods For Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1607.03092/) (2016)
- [Non-Negative Matrix Factorizations for Multiplex Network Analysis](https://mlsanity.com/paper/1612.00750/) (2016)
- [Discrete Optimal Graph Clustering](https://mlsanity.com/paper/1904.11266/) (2019)
- [Clustering-aware Graph Construction: A Joint Learning Perspective](https://mlsanity.com/paper/1905.01446/) (2019)

## Built on by (most cited first, 3 of 3)

- [Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey](https://mlsanity.com/paper/2405.03615/) (2024)
- [Semi-supervised Symmetric Non-negative Matrix Factorization with Low-Rank Tensor Representation](https://mlsanity.com/paper/2405.02688/) (2024)
- [Graph-based Clustering Revisited: A Relaxation of Kernel k-Means Perspective](https://mlsanity.com/paper/2509.18826/) (2025)

## Abstract (arXiv)

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of variables. Inspired by ensemble clustering that aims to seek a better clustering result from a set of clustering results, we propose self-supervised SNMF (S3NMF), which is capable of boosting clustering performance progressively by taking advantage of the sensitivity to initialization characteristic of SNMF, without relying on any additional information. Specifically, we first perform SNMF repeatedly with a random nonnegative matrix for initialization each time, leading to multiple decomposed matrices. Then, we rank the quality of the resulting matrices with adaptively learned weights, from which a new similarity matrix that is expected to be more discriminative is reconstructed for SNMF again. These two steps are iterated until the stopping criterion/maximum number of iterations is achieved. We mathematically formulate S3NMF as a constraint optimization problem, and provide an alternative optimization algorithm to solve it with the theoretical convergence guaranteed. Extensive experimental results on 10 commonly used benchmark datasets demonstrate the significant advantage of our S3NMF over 12 state-of-the-art methods in terms of 5 quantitative metrics. The source code is publicly available at https://github.com/jyh-learning/SSSNMF.