Yu Song

Yu Song, Yiquan Wu

The problem of fitting a union of subspaces to a collection of data points drawn from multiple subspaces is considered in this paper. In the traditional low rank representation model, the dictionary used to represent the data points is chosen as the data points themselves and thus the dictionary is corrupted with noise. This problem is solved in the low rank subspace clustering model which decomposes the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and gross errors. Also, the clustering results of the low rank representation model can be enhanced by using a graph of data similarity. This model is called Laplacian regularized low rank representation model with a graph regularization term added to the objective function. Inspired from the above two ideas, in this paper a Laplacian regularized low rank subspace clustering model is proposed. This model uses a clean dictionary to represent the data points and a graph regularization term is also incorporated in the objective function. Experimental results show that, compared with the traditional low rank representation model, low rank subspace clustering model and several other state-of-the-art subspace clustering model, the model proposed in this paper can get better subspace clustering results with lower clustering error.

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.