Robust and Efficient Subspace Segmentation via Least Squares Regression

Abstract

Abstract. This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much attention. If the subspaces from which the data drawn are independent or orthogonal, they are able to obtain a block diagonal affinity matrix, which usually leads to a correct segmentation. The main differences among them are their objective functions. We theoretically show that if the objective function satisfies some conditions, and the data are sufficiently drawn from independent subspaces, the obtained affinity matrix is always block diagonal. Furthermore, the data sampling can be insufficient if the subspaces are orthogonal. Some existing methods are all special cases. Then we present the Least Squares Regression (LSR) method for subspace segmentation. It takes advantage of data correlation, which is common in real data. LSR encourages a grouping effect which tends to group highly correlated data together. Experimental results on the Hopkins 155 database and Extended Yale Database B show that our method significantly outperforms stateof-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.

Robust subspace clustering via joint weighted Schatten- p norm and Lq norm minimization

“…We conduct face clustering experiments on the extended Yale B and AR dataset and motion segmentation experiments on the Hopkins155 dataset. WSPQ is compared to several related subspace clustering methods, including principal component analysis (PCA), local subspace affinity (LSA), 15 spectral curvature clustering (SCC), 16 least squares regression (LSR), 46 low rank subspace clustering (LRSC), 47 Schatten-p norm regularized LRR (SPM), 40 SSC, 21 and LRR. 28 All the experiments are conducted using MATLAB ® 2012a in a laptop with Intel Core i7 4710MQ CPU and 8GRAM.…”

Symmetric low-rank representation for subspace clustering

“…The SLRR was inspired by collaborative representation and low-rank representation techniques, which are used in classification and subspace clustering [2,38,39]. This proposed technique identifies clusters using the angular information of the principal directions of the symmetric low-rank representation, which preserves the low-rank subspace structures.…”

“…In the absence of noise, i.e., the samples are strictly drawn from multiple subspaces, several criteria are imposed on the optimization models to learn the representation of samples as an affinity matrix for spectral clustering to solve the subspace clustering problem exactly [2,4,39,40]. For example, SSC employs the sparsest representation using an l 1 -norm regularization, while LRR seeks to learn the lowest-rank representation using a nuclear-norm regularization.…”

“…Figure 1 shows an intuitive clustering example using five subjects to illustrate our approach. Owing to the self-expressiveness property of the data, our motivation starts from an observation of collaborative representation, which plays an important role in classification and clustering tasks [38,39]. In particular, our motivation is to integrate the collaborative representation combined with low-rank matrix recovery techniques into a low-rank representation to learn a symmetric low-rank representation.…”

Robust Face Recognition via Adaptive Sparse Representation

“…In [38], Zhang pointed out that the success of SRC comes from the collaborative representation of y over all training samples. The 2 -norm is supposed to take advantage of data correlation [39]. Thus, the query image y is represented by the over-complete dictionary with 2 -norm rather than 1 -norm to constrain the coding vector in CRC.…”