Subspace clustering based on low rank representation and weighted nuclear norm minimization

TL;DR

This paper introduces a novel subspace clustering method using weighted nuclear norm minimization to improve the accuracy of data segmentation into multiple linear subspaces.

Contribution

It proposes the use of weighted nuclear norm instead of standard nuclear norm in low rank representation for better approximation of matrix rank, enhancing clustering performance.

Findings

WNNM-LRR achieves higher clustering accuracy than existing methods.

Experimental results validate the effectiveness of weighted nuclear norm in subspace clustering.

The proposed methods outperform several state-of-the-art algorithms.

Abstract

Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed and low rank representation based subspace clustering is a very promising and efficient subspace clustering algorithm. Low rank representation method seeks the lowest rank representation among all the candidates that can represent the data points as linear combinations of the bases in a given dictionary. Nuclear norm minimization is adopted to minimize the rank of the representation matrix. However, nuclear norm is not a very good approximation of the rank of a matrix and the representation matrix thus obtained can be of high rank which will affect the final clustering accuracy. Weighted nuclear norm (WNN) is a better approximation of the rank of a matrix and WNN is adopted in this paper to describe the rank of the representation matrix. The convex program is solved via conventional alternation direction method of multipliers (ADMM) and linearized alternating direction method of multipliers (LADMM) and they are respectively refer to as WNNM-LRR and WNNM-LRR(L). Experimental results show that, compared with low rank representation method and several other state-of-the-art subspace clustering methods, WNNM-LRR and WNNM-LRR(L) can get higher clustering accuracy.