  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.
