mlsanityData to 14 Oct 2026

Robust and Efficient Subspace Segmentation via Least Squares Regression

arXiv 1404.6736 ↗First posted 27 Apr 2014cs.CVcited by 47

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Abstract (arXiv)

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much attention. If the subspaces from which the data drawn are independent or orthogonal, they are able to obtain a block diagonal affinity matrix, which usually leads to a correct segmentation. The main differences among them are their objective functions. We theoretically show that if the objective function satisfies some conditions, and the data are sufficiently drawn from independent subspaces, the obtained affinity matrix is always block diagonal. Furthermore, the data sampling can be insufficient if the subspaces are orthogonal. Some existing methods are all special cases. Then we present the Least Squares Regression (LSR) method for subspace segmentation. It takes advantage of data correlation, which is common in real data. LSR encourages a grouping effect which tends to group highly correlated data together. Experimental results on the Hopkins 155 database and Extended Yale Database B show that our method significantly outperforms state-of-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.

Key facts. Cited by 47 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 Apr 2014.

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Citing papers per year: 2021: 13; 2022: 8; 2023: 11; 2024: 6; 2025: 7; 2026: 2.

47 papers.

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  1. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  2. 2022Deep Clustering: A Comprehensive Surveycited by 78
  3. 2021Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-viewcited by 30
  4. 2021Pseudo-supervised Deep Subspace Clusteringcited by 29
  5. 2021Learning a Self-Expressive Network for Subspace Clusteringcited by 24
  6. 2024Graph Condensation: A Surveycited by 23
  7. 2023Image Clustering via the Principle of Rate Reduction in the Age of Pretrained Modelscited by 22
  8. 2023Unpaired Multi-View Graph Clustering with Cross-View Structure Matchingcited by 19
  9. 2025Learning segmentation from point trajectoriescited by 15
  10. 2021Towards Clustering-friendly Representations: Subspace Clustering via Graph Filteringcited by 14
  11. 2023A Novel Approach for Effective Multi-View Clustering with Information-Theoretic Perspectivecited by 14
  12. 2023Unsupervised Manifold Linearizing and Clusteringcited by 12
35 more
  1. 2021A Simple Approach to Automated Spectral Clusteringcited by 10
  2. 2025A Comprehensive Survey on Spectral Clustering with Graph Structure Learningcited by 10
  3. 2021Adaptive Attribute and Structure Subspace Clustering Networkcited by 9
  4. 2022Consistency and Diversity induced Human Motion Segmentationcited by 7
  5. 2025Exploring a Principled Framework for Deep Subspace Clusteringcited by 7
  6. 2021Large-Scale Hyperspectral Image Clustering Using Contrastive Learningcited by 6
  7. 2024Spectral Subspace Clustering for Attributed Graphscited by 6
  8. 2024Nonlinear subspace clustering by functional link neural networkscited by 5
  9. 2021Graph Constrained Data Representation Learning for Human Motion Segmentationcited by 4
  10. 2023Adaptive Graph Convolutional Subspace Clusteringcited by 4
  11. 2023Deep Double Self-Expressive Subspace Clusteringcited by 3
  12. 2024Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problemscited by 3
  13. 2022Learning idempotent representation for subspace clusteringcited by 2
  14. 2021PMSSC: Parallelizable multi-subset based self-expressive model for subspace clusteringcited by 1
  15. 2021Attentive Multi-View Deep Subspace Clustering Netcited by 1
  16. 2022C2IMUFS: Complementary and Consensus Learning-based Incomplete Multi-view Unsupervised Feature Selectioncited by 1
  17. 2023Hyper-Laplacian Regularized Concept Factorization in Low-rank Tensor Space for Multi-view Clusteringcited by 1
  18. 2024Graph Cuts with Arbitrary Size Constraints Through Optimal Transportcited by 1
  19. 2024Contrastive Learning Subspace for Text Clusteringcited by 1
  20. 2025Temporal Rate Reduction Clustering for Human Motion Segmentationcited by 1
  21. 2021Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithmscited by 0
  22. 2021Weighted Sparse Subspace Representation: A Unified Framework for Subspace Clustering, Constrained Clustering, and Active Learningcited by 0
  23. 2021Learning Deep Representation with Energy-Based Self-Expressiveness for Subspace Clusteringcited by 0
  24. 2022Fusion Subspace Clustering for Incomplete Datacited by 0
  25. 2022Self-Supervised Deep Subspace Clustering with Entropy-normcited by 0
  26. 2022Revisiting data augmentation for subspace clusteringcited by 0
  27. 2023One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clusteringcited by 0
  28. 2023Learning Structure Aware Deep Spectral Embeddingcited by 0
  29. 2023Interpretable Neural Embeddings with Sparse Self-Representationcited by 0
  30. 2023Efficient and Effective Deep Multi-view Subspace Clusteringcited by 0
  31. 2025Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approachcited by 0
  32. 2025A Joint Sparse Self-Representation Learning Method for Multiview Clusteringcited by 0
  33. 2025Scalable Deep Subspace Clustering Networkcited by 0
  34. 2026Jointly Learning Structured Representations and Stabilized Affinity for Human Motion Segmentationcited by 0
  35. 2026D-CLOT: Double Closed Loop Optimal Transport for Unsupervised Action Segmentationcited by 0