# Semi-supervised Symmetric Non-negative Matrix Factorization with Low-Rank Tensor Representation

arXiv: https://arxiv.org/abs/2405.02688 · HTML: https://mlsanity.com/paper/2405.02688/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 4 May 2024.

## Builds on (most cited first, 10 of 10)

- [Deep Co-Training for Semi-Supervised Image Recognition](https://mlsanity.com/paper/1803.05984/) (2018)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [A General Analysis of the Convergence of ADMM](https://mlsanity.com/paper/1502.02009/) (2015)
- [Multi-View Spectral Clustering Tailored Tensor Low-Rank Representation](https://mlsanity.com/paper/2004.14705/) (2020)
- [Projection onto the capped simplex](https://mlsanity.com/paper/1503.01002/) (2015)
- [Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation](https://mlsanity.com/paper/2205.10481/) (2022)
- [Joint Projection Learning and Tensor Decomposition Based Incomplete Multi-view Clustering](https://mlsanity.com/paper/2310.04038/) (2023)
- [A Note on the Convergence of ADMM for Linearly Constrained Convex Optimization Problems](https://mlsanity.com/paper/1507.02051/) (2015)
- [Self-supervised Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2103.01689/) (2021)

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

- [AdaptGCD: Multi-Expert Adapter Tuning for Generalized Category Discovery](https://mlsanity.com/paper/2410.21705/) (2024)
- [Robust Orthogonal NMF with Label Propagation for Image Clustering](https://mlsanity.com/paper/2504.21472/) (2025)

## Abstract (arXiv)

Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes the available supervisory information (usually in the form of pairwise constraints) to improve the clustering ability of SNMF. The previous methods introduce the pairwise constraints from the local perspective, i.e., they either directly refine the similarity matrix element-wisely or restrain the distance of the decomposed vectors in pairs according to the pairwise constraints, which overlook the global perspective, i.e., in the ideal case, the pairwise constraint matrix and the ideal similarity matrix possess the same low-rank structure. To this end, we first propose a novel semi-supervised SNMF model by seeking low-rank representation for the tensor synthesized by the pairwise constraint matrix and a similarity matrix obtained by the product of the embedding matrix and its transpose, which could strengthen those two matrices simultaneously from a global perspective. We then propose an enhanced SNMF model, making the embedding matrix tailored to the above tensor low-rank representation. We finally refine the similarity matrix by the strengthened pairwise constraints. We repeat the above steps to continuously boost the similarity matrix and pairwise constraint matrix, leading to a high-quality embedding matrix. Extensive experiments substantiate the superiority of our method. The code is available at https://github.com/JinaLeejnl/TSNMF.