mlsanityData to 7 Oct 2026

Noisy Sparse Subspace Clustering

arXiv 1309.1233 ↗First posted 5 Sep 2013stat.MLcited by 18

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Abstract (arXiv)

This paper considers the problem of subspace clustering under noise. Specifically, we study the behavior of Sparse Subspace Clustering (SSC) when either adversarial or random noise is added to the unlabelled input data points, which are assumed to be in a union of low-dimensional subspaces. We show that a modified version of SSC is provably effective in correctly identifying the underlying subspaces, even with noisy data. This extends theoretical guarantee of this algorithm to more practical settings and provides justification to the success of SSC in a class of real applications.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Sep 2013.

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Citing papers per year: 2021: 4; 2022: 8; 2023: 3; 2024: 2; 2025: 1.

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  1. 2024Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributionscited by 53
  2. 2021Learning a Self-Expressive Network for Subspace Clusteringcited by 24
  3. 2023Unsupervised Manifold Linearizing and Clusteringcited by 12
  4. 2023Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustnesscited by 11
  5. 2021A Simple Approach to Automated Spectral Clusteringcited by 10
  6. 2022Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clusteringcited by 9
  7. 2025Exploring a Principled Framework for Deep Subspace Clusteringcited by 7
  8. 2021Popularity Adjusted Block Models are Generalized Random Dot Product Graphscited by 4
  9. 2022Sparse Subspace Clustering in Diverse Multiplex Network Modelcited by 4
  10. 2021Provable Data Clustering via Innovation Searchcited by 1
  11. 2022Greedier is Better: Selecting Multiple Neighbors per Iteration for Sparse Subspace Clusteringcited by 1
  12. 2022Provable Clustering of a Union of Linear Manifolds Using Optimal Directionscited by 0
6 more
  1. 2022Fusion Subspace Clustering for Incomplete Datacited by 0
  2. 2022Noisy ℓ0-Sparse Subspace Clustering on Dimensionality Reduced Datacited by 0
  3. 2022Revisiting data augmentation for subspace clusteringcited by 0
  4. 2022Variable Clustering via Distributionally Robust Nodewise Regressioncited by 0
  5. 2023Sketching for Convex and Nonconvex Regularized Least Squares with Sharp Guaranteescited by 0
  6. 2024Locally Regularized Sparse Graph by Fast Proximal Gradient Descentcited by 0