Active Orthogonal Matching Pursuit for Sparse Subspace Clustering

TL;DR

This paper introduces Active OMP-SSC, an improved greedy pursuit algorithm for sparse subspace clustering that enhances accuracy by adaptively updating and dropping data points, maintaining low computational complexity.

Contribution

It proposes a novel Active OMP-SSC method that adaptively updates and drops data points during clustering to improve accuracy while keeping computational costs low.

Findings

Active OMP-SSC outperforms traditional OMP-SSC in clustering accuracy.

The method maintains low computational complexity similar to greedy algorithms.

Numerical experiments validate the effectiveness of the proposed approach.

Abstract

Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high computational complexity, other variants of SSC, such as Orthogonal Matching Pursuit-based SSC (OMP-SSC), lose clustering accuracy in pursuit of improving time efficiency. In this letter, we propose a novel Active OMP-SSC, which improves clustering accuracy of OMP-SSC by adaptively updating data points and randomly dropping data points in the OMP process, while still enjoying the low computational complexity of greedy pursuit algorithms. We provide heuristic analysis of our approach, and explain how these two active steps achieve a better tradeoff between connectivity and separation. Numerical results on both synthetic data and real-world data validate our analyses and show the advantages of the proposed active algorithm.