Research On Dimensionality Reduction Algorithm Based On Sparse Representation

With the speedy development and extensive application of information science technology, data with high dimension and nonlinear structure emerged in multitude. However, the high-dimensional data are always difficult to process in procedure of pattern recognition and machine learning. The reasons are:(1) the so called "curse of dimensionality" is usually a major cause of limitations of many practical technologies;(2) high dimensionality needs more storage and computational cost. Therefore, the topic research on dimensionality reduction (DR) of data has always been momentous in related scientific fields.Over the past several decades, many DR methods including linear DR methods and non-linear DR methods have been proposed and studied. There are several common methods such as, traditional Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA); some representative manifold learning methods like Locally Linear Embedding (LLE), Isometric Mapping (ISOMAP), Laplacian Eigenmaps (LE) and Local Tangent Space Alignment (LTSA). However, many existed algorithms have lots of drawbacks, for example, PCA is lack of discriminating power; LDA suffers from small sample size (SSS) problem; manifold algorithms like LLE cannot apply to recognition problem; and so on. Therefore, in this paper, we mainly focus on the research of sparse representation (SR) theory based dimensionality reduction methods. This paper aims to obtain effective feasible algorithms to improve the performance of face recognition. The main contributions of this paper including:(1) This paper comprehensively analyzes the research background, significance, status and challenges of current DR problem.(2) By introducing between-class weight matrix and within-class weight matrix, we propose a novel supervised linear dimensionality reduction method named Linear Discriminant Projection (LDP). Not only does LDP maximize the separability of different submanifolds and minimize the compactness of local submanifolds, but also LDP preserves the local neighborhood structure of the data in low-dimensional subspace. Simultaneously, LDP overcomes the SSS problem. Additionally, LDP is robust to outliers.(3) By incorporating between-class scatter and within-class scatter into the NPE algorithm, we propose a discriminating neighborhood preserving embedding (DNPE) algorithm. By imposing a discriminating limitation to improve the discriminant power of DNPE, we effectively improve the performance of face recognition and the practical performance of DNPE.(4) Inspired by sparse representation (SR) theory, we propose a new SR based algorithm called Sparse Discriminating Neighborhood Preserving Embedding (SDNPE). SDNPE directly computes the weight matrix by sparse reconstruction without constructing adjacency graphs, which avoids the disturbance of too many parameters and greatly improves the performance of recognition.Experimental results on ORL, Yale, AR and Extended YaleB face databases verify the efficacy of the proposed three methods.