Studies On Sparse Coding And Its Applications In Pattern Recognition

Sparse coding is a cross-field research including neurobiology, psychology and computer science. Recently, an in-depth study has been carried out by many scientists and a lot of important research results have been obtained. Based on the study of sparse coding, human perception system can be simulated by the computer to a certain extent, which has important practical value in the field of human intelligence and pattern recognition.In the field of pattern recognition, sparse representation (SR) is considered as a new valid and robust feature representation and has been successfully applied in a great deal of practical problems. Based on the sparse coding theory, a series of sparse regularized model are proposed in this dissertation, focusing on many frontier researches in the field of pattern recognition, such as manifold learning, regression problem and subspace clustering. The major contributions of this dissertation are as follows:1) A comprehensive study on the sparse coding theory is carried out, especially on the sparse characteristics. Introduce a classical sparse regularized problem, called as Lasso problem. A brief summary about the performances of a traditional optimization method and newly proposed fast optimization methods for solving the Lasso problem is given in detail.2) Since the local structure constructing process of current manifold learning methods is too limited and always lacks robustness to data noise, a (?)1-graph regularized semi-supervised manifold learning method (LRSML) is proposed in this dissertation for this problem. Normally, the neighborhood and local structure of the data set are constructed based on the Euclidean distance. However, the data structure is always corrupted in the Euclidean space due to a variety of data noise. Robustness must be considered by a mature manifold learning method. In the learning process of LRSML model, two graphs are constructed. One is KNN-graph based on the Euclidean distance, the other is e1-graph based on the sparse representation. LRSML model can be considered as a valid combination of Laplacian Eigenmaps (LE) method and sparse coding. Experimental results show that LRSML method can indeed construct the nature low-dimentional structure of data. Furthermore, a linear LRSML (L-LRSML) version is proposed to obtain the low-dimensional representation of new test data. L-LRSML aims at constructing the optimal linear projection which preserves the manifold structure. Compared to current linear dimensionality reduction methods, L-LRSML presents a better performance for face recognition problem.3) Current regression models always lack robustness to the data noise and outliers. A new convex regularized sparse regression (CRSR) method is proposed for this problem based on low-rank and sparse regularizations. CRSR aims at simultaneously removing the noise and outliers from the data and learning the regression model based on the recovered data. CRSR model can be considered as a valid combination of Lasso model and robust principal component analysis. The robustness to data noise and outliers of CRSR model is verified with extensive experiments for head pose estimation problem.4) Current subspace clustering algorithms always lack robustness to data noise. A new refined sparse subspace clustering (RSSC) method is proposed in this dissertation. RSSC aims at simultaneously removing the noise from the data and learning the sparse representation with respect to the recovered over-complete dictionary via low-rank regularization. The sparse representation coefficients depict the similarity between different data samples. The ability of RSSC to recover the low-rank data structure is verified using toy data. Meanwhile, sparseness and block diagonal form of the similarity matrix is presented using RSSC model, which is beneficial to the final data clustering. The experimental results further demonstrate the superiority of our RSSC methods over other state-of-the-art methods for motion segmentation problem.