Low-rank sparse subspace clustering with a clean dictionary. (January 2021)

• Record Type: Journal Article
• Authors: You, Cong-Zhe; Shu, Zhen-Qiu; Fan, Hong-Hui
• Is Part Of: Journal of algorithms & computational technology. Volume 15(2021)
• Publication Date: 2021-01
• Subjects: Subspace clustering -- low-rank representation -- sparse representation; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748302620983690
• Languages: English
• ISSNs: 1748-3018

Abstract

Low-Rank Representation (LRR) and Sparse Subspace Clustering (SSC) are considered as the hot topics of subspace clustering algorithms. SSC induces the sparsity through minimizing thel 1 -norm of the data matrix while LRR promotes a low-rank structure through minimizing the nuclear norm. In this paper, considering the problem of fitting a union of subspace to a collection of data points drawn from one more subspaces and corrupted by noise, we pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise. We propose a new algorithm, named Low-Rank and Sparse Subspace Clustering with a Clean dictionary (LRS2C2), by combining SSC and LRR, as the representation is often both sparse and low-rank. The effectiveness of the proposed algorithm is demonstrated through experiments on motion segmentation and image clustering.