Data-Adaptive Low-Rank Sparse Subspace Clustering

TL;DR

This paper introduces a data-adaptive low-rank sparse subspace clustering algorithm that improves upon existing methods by incorporating a surrogate for the S0/L0 quasi-norm, with proven convergence and tested on standard datasets.

Contribution

It proposes a novel LRSSC algorithm with a data-adaptive surrogate for the S0/L0 quasi-norm, including a numerical solution for the proximal operator and theoretical convergence proof.

Findings

Outperforms existing LRSSC methods on benchmark datasets

Proven global convergence to a stationary point

Effective handling of data-adaptive sparse structures

Abstract

Low-rank sparse subspace clustering (LRSSC) algorithms built on self-expressive model effectively capture both the global and local structure of the data. However, existing solutions, primarily based on proximal operators associated with Sp/Lp , p e {0, 1/2, 2/3, 1}, norms are not data-adaptive. In this work, we propose an LRSSC algorithm incorporating a data-adaptive surrogate for the S0/L0 quasi-norm. We provide a numerical solution for the corresponding proximal operator in cases where an analytical expression is unavailable. The proposed LRSSC algorithm is formulated within the proximal mapping framework, and we present theoretical proof of its global convergence toward a stationary point. We evaluate the performance of the proposed method on three well known datasets, comparing it against LRSSC algorithms constrained by Sp/Lp, p e {0, 1/2, 2/3, 1}, norms.