mlsanityData to 7 Oct 2026

Robust subspace clustering

arXiv 1301.2603 ↗First posted 11 Jan 2013cs.LG cs.IT math.ITcited by 24

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Abstract (arXiv)

Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2009) 2790-2797] to cluster noisy data, and develops some novel theory demonstrating its correctness. In particular, the theory uses ideas from geometric functional analysis to show that the algorithm can accurately recover the underlying subspaces under minimal requirements on their orientation, and on the number of samples per subspace. Synthetic as well as real data experiments complement our theoretical study, illustrating our approach and demonstrating its effectiveness.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jan 2013.

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Citing papers per year: 2021: 5; 2022: 7; 2023: 3; 2024: 2; 2025: 1; 2026: 6.

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  1. 2024Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributionscited by 53
  2. 2026Do Sparse Autoencoders Capture Concept Manifolds?cited by 25
  3. 2021Learning a Self-Expressive Network for Subspace Clusteringcited by 24
  4. 2022Incremental Learning of Structured Memory via Closed-Loop Transcriptioncited by 17
  5. 2023Unsupervised Manifold Linearizing and Clusteringcited by 12
  6. 2023Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustnesscited by 11
  7. 2021A Simple Approach to Automated Spectral Clusteringcited by 10
  8. 2022Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clusteringcited by 9
  9. 2026Influence-Preserving Proxies for Gradient-Based Data Selection in LLM Fine-tuningcited by 9
  10. 2022The Geometry of Self-supervised Learning Models and its Impact on Transfer Learningcited by 7
  11. 2026Measuring Affinity between Attention-Head Weight Subspaces via the Projection Kernelcited by 5
  12. 2022Sparse Subspace Clustering in Diverse Multiplex Network Modelcited by 4
12 more
  1. 2021PPGN: Physics-Preserved Graph Networks for Real-Time Fault Location in Distribution Systems with Limited Observation and Labelscited by 3
  2. 2026Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifoldscited by 3
  3. 2022Greedier is Better: Selecting Multiple Neighbors per Iteration for Sparse Subspace Clusteringcited by 1
  4. 2021Imperceptible Adversarial Examples for Fake Image Detectioncited by 0
  5. 2021Convex Latent Effect Logit Model via Sparse and Low-rank Decompositioncited by 0
  6. 2022Fusion Subspace Clustering for Incomplete Datacited by 0
  7. 2022Variable Clustering via Distributionally Robust Nodewise Regressioncited by 0
  8. 2023Open-World Object Detection via Discriminative Class Prototype Learningcited by 0
  9. 2024Locally Regularized Sparse Graph by Fast Proximal Gradient Descentcited by 0
  10. 2025Affine Subspace Models and Clustering for Patch-Based Image Denoisingcited by 0
  11. 2026Semantic Purification for Conditional Representation Learningcited by 0
  12. 2026Clustering as Approximation by Constrained Projectors: Theory and Guaranteescited by 0