# Robust subspace clustering

arXiv: https://arxiv.org/abs/1301.2603 · HTML: https://mlsanity.com/paper/1301.2603/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2013.

## Built on by (most cited first, 24 of 24)

- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [Incremental Learning of Structured Memory via Closed-Loop Transcription](https://mlsanity.com/paper/2202.05411/) (2022)
- [Unsupervised Manifold Linearizing and Clustering](https://mlsanity.com/paper/2301.01805/) (2023)
- [Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustness](https://mlsanity.com/paper/2309.16096/) (2023)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [Influence-Preserving Proxies for Gradient-Based Data Selection in LLM Fine-tuning](https://mlsanity.com/paper/2602.17835/) (2026)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [The Geometry of Self-supervised Learning Models and its Impact on Transfer Learning](https://mlsanity.com/paper/2209.08622/) (2022)
- [Measuring Affinity between Attention-Head Weight Subspaces via the Projection Kernel](https://mlsanity.com/paper/2601.10266/) (2026)
- [Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds](https://mlsanity.com/paper/2606.25234/) (2026)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [PPGN: Physics-Preserved Graph Networks for Real-Time Fault Location in Distribution Systems with Limited Observation and Labels](https://mlsanity.com/paper/2107.02275/) (2021)
- [Greedier is Better: Selecting Multiple Neighbors per Iteration for Sparse Subspace Clustering](https://mlsanity.com/paper/2204.02572/) (2022)
- [Imperceptible Adversarial Examples for Fake Image Detection](https://mlsanity.com/paper/2106.01615/) (2021)
- [Convex Latent Effect Logit Model via Sparse and Low-rank Decomposition](https://mlsanity.com/paper/2108.09859/) (2021)
- [Fusion Subspace Clustering for Incomplete Data](https://mlsanity.com/paper/2205.10872/) (2022)
- [Variable Clustering via Distributionally Robust Nodewise Regression](https://mlsanity.com/paper/2212.07944/) (2022)
- [Open-World Object Detection via Discriminative Class Prototype Learning](https://mlsanity.com/paper/2302.11757/) (2023)
- [Locally Regularized Sparse Graph by Fast Proximal Gradient Descent](https://mlsanity.com/paper/2409.17090/) (2024)
- [Affine Subspace Models and Clustering for Patch-Based Image Denoising](https://mlsanity.com/paper/2512.07259/) (2025)
- [Semantic Purification for Conditional Representation Learning](https://mlsanity.com/paper/2602.05464/) (2026)
- [Clustering as Approximation by Constrained Projectors: Theory and Guarantees](https://mlsanity.com/paper/2608.29102/) (2026)

## 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.