# Essential Tensor Learning for Multi-view Spectral Clustering

arXiv: https://arxiv.org/abs/1807.03602 · HTML: https://mlsanity.com/paper/1807.03602/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2018.

## Built on by (most cited first, 30 of 31)

- [Graph Contrastive Clustering](https://mlsanity.com/paper/2104.01429/) (2021)
- [Effective and Efficient Graph Learning for Multi-view Clustering](https://mlsanity.com/paper/2108.06734/) (2021)
- [Self-Supervised Information Bottleneck for Deep Multi-View Subspace Clustering](https://mlsanity.com/paper/2204.12496/) (2022)
- [Hybrid-Supervised Dual-Search: Leveraging Automatic Learning for Loss-free Multi-Exposure Image Fusion](https://mlsanity.com/paper/2309.01113/) (2023)
- [Fearless Luminance Adaptation: A Macro-Micro-Hierarchical Transformer for Exposure Correction](https://mlsanity.com/paper/2309.00872/) (2023)
- [Joint Projection Learning and Tensor Decomposition Based Incomplete Multi-view Clustering](https://mlsanity.com/paper/2310.04038/) (2023)
- [Manifold-based Incomplete Multi-view Clustering via Bi-Consistency Guidance](https://mlsanity.com/paper/2405.10987/) (2024)
- [Adaptively Topological Tensor Network for Multi-view Subspace Clustering](https://mlsanity.com/paper/2305.00716/) (2023)
- [Holistic Dynamic Frequency Transformer for Image Fusion and Exposure Correction](https://mlsanity.com/paper/2309.01183/) (2023)
- [ASF-Net: Robust Video Deraining via Temporal Alignment and Online Adaptive Learning](https://mlsanity.com/paper/2309.00956/) (2023)
- [Dual Information Enhanced Multi-view Attributed Graph Clustering](https://mlsanity.com/paper/2211.14987/) (2022)
- [AdvMono3D: Advanced Monocular 3D Object Detection with Depth-Aware Robust Adversarial Training](https://mlsanity.com/paper/2309.01106/) (2023)
- [Trash to Treasure: Low-Light Object Detection via Decomposition-and-Aggregation](https://mlsanity.com/paper/2309.03548/) (2023)
- [Label Learning Method Based on Tensor Projection](https://mlsanity.com/paper/2402.16544/) (2024)
- [Multiple Graph Learning for Scalable Multi-view Clustering](https://mlsanity.com/paper/2106.15382/) (2021)
- [Fine-grained Graph Learning for Multi-view Subspace Clustering](https://mlsanity.com/paper/2201.04604/) (2022)
- [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)
- [Enhancing Infrared Small Target Detection Robustness with Bi-Level Adversarial Framework](https://mlsanity.com/paper/2309.01099/) (2023)
- [Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering](https://mlsanity.com/paper/2509.18653/) (2025)
- [Incremental Unsupervised Feature Selection for Dynamic Incomplete Multi-view Data](https://mlsanity.com/paper/2204.02973/) (2022)
- [Adaptive incomplete multi-view learning via tensor graph completion](https://mlsanity.com/paper/2208.03710/) (2022)
- [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)
- [A low-rank non-convex norm method for multiview graph clustering](https://mlsanity.com/paper/2312.11157/) (2023)
- [Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model](https://mlsanity.com/paper/2402.10677/) (2024)
- [One-Step Multi-View Clustering Based on Transition Probability](https://mlsanity.com/paper/2403.01460/) (2024)
- [Tensor-based Graph Learning with Consistency and Specificity for Multi-view Clustering](https://mlsanity.com/paper/2403.18393/) (2024)
- [Interpretable Multi-View Clustering Based on Anchor Graph Tensor Factorization](https://mlsanity.com/paper/2404.00883/) (2024)
- [Fast Disentangled Slim Tensor Learning for Multi-view Clustering](https://mlsanity.com/paper/2411.07685/) (2024)

## Abstract (arXiv)

Multi-view clustering attracts much attention recently, which aims to take advantage of multi-view information to improve the performance of clustering. However, most recent work mainly focus on self-representation based subspace clustering, which is of high computation complexity. In this paper, we focus on the Markov chain based spectral clustering method and propose a novel essential tensor learning method to explore the high order correlations for multi-view representation. We first construct a tensor based on multi-view transition probability matrices of the Markov chain. By incorporating the idea from robust principle component analysis, tensor singular value decomposition (t-SVD) based tensor nuclear norm is imposed to preserve the low-rank property of the essential tensor, which can well capture the principle information from multiple views. We also employ the tensor rotation operator for this task to better investigate the relationship among views as well as reduce the computation complexity. The proposed method can be efficiently optimized by the alternating direction method of multipliers~(ADMM). Extensive experiments on six real world datasets corresponding to five different applications show that our method achieves superior performance over other state-of-the-art methods.