Noisy Sparse Subspace Clustering

TL;DR

This paper analyzes the robustness of Sparse Subspace Clustering (SSC) under noisy conditions, demonstrating that a modified SSC can reliably identify subspaces even with adversarial or random noise, thus extending its practical applicability.

Contribution

It provides a theoretical guarantee for a modified SSC algorithm's effectiveness in noisy environments, enhancing understanding of its robustness in real-world scenarios.

Findings

Modified SSC is provably effective with noisy data

Theoretical guarantees extend to adversarial and random noise

Supports practical success of SSC in real applications

Abstract

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 \emph{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.