# Noisy Sparse Subspace Clustering

arXiv: https://arxiv.org/abs/1309.1233 · HTML: https://mlsanity.com/paper/1309.1233/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2013.

## Built on by (most cited first, 18 of 18)

- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [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)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [Exploring a Principled Framework for Deep Subspace Clustering](https://mlsanity.com/paper/2503.17288/) (2025)
- [Popularity Adjusted Block Models are Generalized Random Dot Product Graphs](https://mlsanity.com/paper/2109.04010/) (2021)
- [Sparse Subspace Clustering in Diverse Multiplex Network Model](https://mlsanity.com/paper/2206.07602/) (2022)
- [Provable Data Clustering via Innovation Search](https://mlsanity.com/paper/2108.06888/) (2021)
- [Greedier is Better: Selecting Multiple Neighbors per Iteration for Sparse Subspace Clustering](https://mlsanity.com/paper/2204.02572/) (2022)
- [Provable Clustering of a Union of Linear Manifolds Using Optimal Directions](https://mlsanity.com/paper/2201.02745/) (2022)
- [Fusion Subspace Clustering for Incomplete Data](https://mlsanity.com/paper/2205.10872/) (2022)
- [Noisy ℓ0-Sparse Subspace Clustering on Dimensionality Reduced Data](https://mlsanity.com/paper/2206.11079/) (2022)
- [Revisiting data augmentation for subspace clustering](https://mlsanity.com/paper/2207.09728/) (2022)
- [Variable Clustering via Distributionally Robust Nodewise Regression](https://mlsanity.com/paper/2212.07944/) (2022)
- [Sketching for Convex and Nonconvex Regularized Least Squares with Sharp Guarantees](https://mlsanity.com/paper/2311.01806/) (2023)
- [Locally Regularized Sparse Graph by Fast Proximal Gradient Descent](https://mlsanity.com/paper/2409.17090/) (2024)

## 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.