Noisy Subspace Clustering via Thresholding

TL;DR

This paper analyzes the effectiveness of the thresholding-based subspace clustering (TSC) algorithm in noisy high-dimensional data, demonstrating its success even with intersecting subspaces and outliers, and establishing explicit noise-affinity tradeoffs.

Contribution

It provides a probabilistic performance analysis of TSC in noisy conditions, revealing explicit noise-affinity tradeoffs and confirming the outlier detection scheme's effectiveness.

Findings

TSC succeeds in noisy cases with intersecting subspaces.

Explicit tradeoff between noise level and subspace affinity is established.

Outlier detection scheme is provably effective in noisy scenarios.

Abstract

We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic performance analysis of the thresholding-based subspace clustering (TSC) algorithm introduced recently in [1] shows that TSC succeeds in the noisy case, even when the subspaces intersect. Our results reveal an explicit tradeoff between the allowed noise level and the affinity of the subspaces. We furthermore find that the simple outlier detection scheme introduced in [1] provably succeeds in the noisy case.