# On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization

arXiv: https://arxiv.org/abs/1610.07126 · HTML: https://mlsanity.com/paper/1610.07126/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2016.

## Built on by (most cited first, 25 of 25)

- [Effective and Efficient Graph Learning for Multi-view Clustering](https://mlsanity.com/paper/2108.06734/) (2021)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [Contrastive Multi-view Subspace Clustering of Hyperspectral Images based on Graph Convolutional Networks](https://mlsanity.com/paper/2312.06068/) (2023)
- [Multi-view MERA Subspace Clustering](https://mlsanity.com/paper/2305.09095/) (2023)
- [Tensor-based Multi-view Spectral Clustering via Shared Latent Space](https://mlsanity.com/paper/2207.11559/) (2022)
- [Joint Projection Learning and Tensor Decomposition Based Incomplete Multi-view Clustering](https://mlsanity.com/paper/2310.04038/) (2023)
- [Adaptively Topological Tensor Network for Multi-view Subspace Clustering](https://mlsanity.com/paper/2305.00716/) (2023)
- [Dual Information Enhanced Multi-view Attributed Graph Clustering](https://mlsanity.com/paper/2211.14987/) (2022)
- [Fine-grained Graph Learning for Multi-view Subspace Clustering](https://mlsanity.com/paper/2201.04604/) (2022)
- [Multi-View Clustering from the Perspective of Mutual Information](https://mlsanity.com/paper/2302.08743/) (2023)
- [Hyper-Laplacian Regularized Concept Factorization in Low-rank Tensor Space for Multi-view Clustering](https://mlsanity.com/paper/2304.11435/) (2023)
- [Rethinking k-means from manifold learning perspective](https://mlsanity.com/paper/2305.07213/) (2023)
- [A Nested Matrix-Tensor Model for Noisy Multi-view Clustering](https://mlsanity.com/paper/2305.19992/) (2023)
- [Generalized Trusted Multi-view Classification Framework with Hierarchical Opinion Aggregation](https://mlsanity.com/paper/2411.03713/) (2024)
- [Towards Comprehensive Information-theoretic Multi-view Learning](https://mlsanity.com/paper/2509.02084/) (2025)
- [Error-Robust Multi-View Clustering: Progress, Challenges and Opportunities](https://mlsanity.com/paper/2105.03058/) (2021)
- [Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clustering](https://mlsanity.com/paper/2210.12638/) (2022)
- [High-dimensional multi-view clustering methods](https://mlsanity.com/paper/2303.08582/) (2023)
- [Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation](https://mlsanity.com/paper/2307.09055/) (2023)
- [TCGF: A unified tensorized consensus graph framework for multi-view representation learning](https://mlsanity.com/paper/2309.09987/) (2023)
- [Tensor-based Graph Learning with Consistency and Specificity for Multi-view Clustering](https://mlsanity.com/paper/2403.18393/) (2024)
- [Subspace Clustering in Wavelet Packets Domain](https://mlsanity.com/paper/2406.03819/) (2024)
- [Fast Disentangled Slim Tensor Learning for Multi-view Clustering](https://mlsanity.com/paper/2411.07685/) (2024)
- [Adversarial Graph Fusion for Incomplete Multi-view Semi-supervised Learning with Tensorial Imputation](https://mlsanity.com/paper/2509.15955/) (2025)
- [Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning](https://mlsanity.com/paper/2607.25295/) (2026)

## Abstract (arXiv)

In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to capture the low rank tensor subspace so that the refinement of the view-specific subspaces can be achieved, as well as the high order correlations underlying multi-view data can be explored. By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) citekilmer13, we can impose a new type of low-rank tensor constraint on the rotated tensor to capture the complementary information from multiple views. Different from traditional unfolding based tensor norm, this low-rank tensor constraint has optimality properties similar to that of matrix rank derived from SVD, so the complementary information among views can be explored more efficiently and thoroughly. The established model, called t-SVD based Multi-view Subspace Clustering (t-SVD-MSC), falls into the applicable scope of augmented Lagrangian method, and its minimization problem can be efficiently solved with theoretical convergence guarantee and relatively low computational complexity. Extensive experimental testing on eight challenging image dataset shows that the proposed method has achieved highly competent objective performance compared to several state-of-the-art multi-view clustering methods.