Optimized Projection for Sparse Representation Based Classification

Dimensionality reduction (DR) methods have been commonly used as a principled way to understand the high-dimensional data such as facial images. In this paper, we propose a new supervised DR method called Optimized Projection for Sparse Representation based Classification (OP-SRC), which is based on the recent face recognition method, Sparse Representation based Classification (SRC). SRC seeks a sparse linear combination on all the training data for a given query image, and make the decision by the minimal reconstruction residual. OP-SRC is designed on the decision rule of SRC, it aims to reduce the within-class reconstruction residual and simultaneously increase the between-class reconstruction residual on the training data. The projections are optimized and match well with the mechanism of SRC. Therefore, SRC performs well in the OP-SRC transformed space. The feasibility and effectiveness of the proposed method is verified on the Yale, ORL and UMIST databases with promising results.

Robust and Efficient Subspace Segmentation via Least Squares Regression

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 state-of-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.