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

Yu Song, Yiquan Wu

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.

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