Accelerated Sparse Subspace Clustering

TL;DR

This paper introduces an accelerated orthogonal least-squares algorithm for sparse subspace clustering, offering a faster and more accurate alternative to existing methods like BP and OMP, especially in high-similarity data scenarios.

Contribution

The paper presents a novel accelerated orthogonal least-squares algorithm that improves efficiency and accuracy in sparse subspace clustering compared to traditional BP and OMP methods.

Findings

The proposed algorithm is faster than BP-based methods.

It achieves higher accuracy than OMP-based schemes.

Under certain conditions, it guarantees subspace-preserving solutions.

Abstract

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practice while the performance of OMP-based schemes are unsatisfactory, especially in settings where data points are highly similar. In this paper, we propose a novel algorithm that exploits an accelerated variant of orthogonal least-squares to efficiently find the underlying subspaces. We show that under certain conditions the proposed algorithm returns a subspace-preserving solution. Simulation results illustrate that the proposed method compares favorably with BP-based method in terms of running time while being significantly more accurate than OMP-based schemes.