# Multi-view Low-rank Sparse Subspace Clustering

arXiv: https://arxiv.org/abs/1708.08732 · HTML: https://mlsanity.com/paper/1708.08732/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2017.

## Built on by (most cited first, 28 of 28)

- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [A Comprehensive Survey on Spectral Clustering with Graph Structure Learning](https://mlsanity.com/paper/2501.13597/) (2025)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)
- [Enhanced Latent Multi-view Subspace Clustering](https://mlsanity.com/paper/2312.14763/) (2023)
- [Rethinking Multi-view Representation Learning via Distilled Disentangling](https://mlsanity.com/paper/2403.10897/) (2024)
- [Scalable Multi-view Clustering with Graph Filtering](https://mlsanity.com/paper/2205.09228/) (2022)
- [Adaptively Topological Tensor Network for Multi-view Subspace Clustering](https://mlsanity.com/paper/2305.00716/) (2023)
- [Disentangling Multi-view Representations Beyond Inductive Bias](https://mlsanity.com/paper/2308.01634/) (2023)
- [Smoothed Multi-View Subspace Clustering](https://mlsanity.com/paper/2106.09875/) (2021)
- [Adaptive Weighted Multi-View Clustering](https://mlsanity.com/paper/2110.13240/) (2021)
- [Multi-level Graph Subspace Contrastive Learning for Hyperspectral Image Clustering](https://mlsanity.com/paper/2404.05211/) (2024)
- [Unsupervised Document and Template Clustering using Multimodal Embeddings](https://mlsanity.com/paper/2506.12116/) (2025)
- [MeanCut: A Greedy-Optimized Graph Clustering via Path-based Similarity and Degree Descent Criterion](https://mlsanity.com/paper/2312.04067/) (2023)
- [Attentive Multi-View Deep Subspace Clustering Net](https://mlsanity.com/paper/2112.12506/) (2021)
- [Enriched Robust Multi-View Kernel Subspace Clustering](https://mlsanity.com/paper/2205.10495/) (2022)
- [Multilayer Graph Approach to Deep Subspace Clustering](https://mlsanity.com/paper/2401.17033/) (2024)
- [Self Supervised Correlation-based Permutations for Multi-View Clustering](https://mlsanity.com/paper/2402.16383/) (2024)
- [Generalized Trusted Multi-view Classification Framework with Hierarchical Opinion Aggregation](https://mlsanity.com/paper/2411.03713/) (2024)
- [Multi-view Subspace Adaptive Learning via Autoencoder and Attention](https://mlsanity.com/paper/2201.00171/) (2022)
- [A low-rank non-convex norm method for multiview graph clustering](https://mlsanity.com/paper/2312.11157/) (2023)
- [Tensor-based Graph Learning with Consistency and Specificity for Multi-view Clustering](https://mlsanity.com/paper/2403.18393/) (2024)
- [Fast and Scalable Semi-Supervised Learning for Multi-View Subspace Clustering](https://mlsanity.com/paper/2408.05707/) (2024)
- [Probabilistically Aligned View-unaligned Clustering with Adaptive Template Selection](https://mlsanity.com/paper/2409.14882/) (2024)
- [Discriminative community detection for multiplex networks](https://mlsanity.com/paper/2410.00724/) (2024)
- [A Joint Sparse Self-Representation Learning Method for Multiview Clustering](https://mlsanity.com/paper/2508.06857/) (2025)
- [Kernel Singular Value Decomposition with Extension to Multiple Data Sources](https://mlsanity.com/paper/2610.03216/) (2026)

## Abstract (arXiv)

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets.