# Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation

arXiv: https://arxiv.org/abs/2205.10481 · HTML: https://mlsanity.com/paper/2205.10481/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 21 May 2022.

## Builds on (most cited first, 6 of 6)

- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [XAI Beyond Classification: Interpretable Neural Clustering](https://mlsanity.com/paper/1808.07292/) (2018)
- [Discriminative Block-Diagonal Representation Learning for Image Recognition](https://mlsanity.com/paper/1707.03548/) (2017)
- [Constrained Sparse Subspace Clustering with Side-Information](https://mlsanity.com/paper/1805.08183/) (2018)

## Built on by (most cited first, 7 of 7)

- [EGRC-Net: Embedding-induced Graph Refinement Clustering Network](https://mlsanity.com/paper/2211.10627/) (2022)
- [Semi-supervised Symmetric Non-negative Matrix Factorization with Low-Rank Tensor Representation](https://mlsanity.com/paper/2405.02688/) (2024)
- [AdaptGCD: Multi-Expert Adapter Tuning for Generalized Category Discovery](https://mlsanity.com/paper/2410.21705/) (2024)
- [Discriminative Anchor Learning for Efficient Multi-view Clustering](https://mlsanity.com/paper/2409.16904/) (2024)
- [Partial Label Clustering](https://mlsanity.com/paper/2505.03207/) (2025)
- [Data-Adaptive Transformed Bilateral Tensor Low-Rank Representation for Clustering](https://mlsanity.com/paper/2510.20077/) (2025)
- [Synergistic Dual-Branch Adaptation for Multi-modal Generalized Category Discovery](https://mlsanity.com/paper/2606.21446/) (2026)

## Abstract (arXiv)

In this letter, we propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. By representing the limited amount of supervisory information as a pairwise constraint matrix, we observe that the ideal affinity matrix for clustering shares the same low-rank structure as the ideal pairwise constraint matrix. Thus, we stack the two matrices into a 3-D tensor, where a global low-rank constraint is imposed to promote the affinity matrix construction and augment the initial pairwise constraints synchronously. Besides, we use the local geometry structure of input samples to complement the global low-rank prior to achieve better affinity matrix learning. The proposed model is formulated as a Laplacian graph regularized convex low-rank tensor representation problem, which is further solved with an alternative iterative algorithm. In addition, we propose to refine the affinity matrix with the augmented pairwise constraints. Comprehensive experimental results on eight commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods. The code is publicly available at https://github.com/GuanxingLu/Subspace-Clustering.