Linear Representation With Structured Information

Linear Representation(LR)-based classifier is a classical machine learning method.Because of its sample but effective,there are many successful applications in areas of pattern recognition and computer vision.However,in recent technology revolutions,there are two main problems for these types of methods: firstly,they assume that the samples from same class distribute in same sub-space.Thus,the queries can be regressed and represented by the samples from same class.In the procedure of regression,the measurement function of traditional algorithms is based on the assumption of features being mutual independence.That ignores the structured information of data what leads poor performances when these methods face some specific data.In the situation of test samples existing large structured noise,the positions of test samples are changed in sub-space of feature.That makes them represented by samples from wrong classes.Secondly,in traditional LR-based method,regression and classification are totally separated course.In the regression part,classifiers do not make use of label information of training set.That leads the coding coefficients of represented samples can not reflect the structure of training samples.Also,coding coefficients turn to unstable while the queries existing large noise.To take full advantage of structured information,this thesis presents a novel LR model from face recognition view.Unlike traditional method,this model adopts bidirection matrix norm instead of vector norm to calculate the representation residuals.Instead of treading each pixel independently,to mine the structured information,pixels from same line(or column)are connected.Moreover,this thesis studies the influences of regularizers in regression.To further improve performance of classifier,the groupsparse regularizer is introduced in our model.Then,this thesis studies the relationship between the half-quadratical minimization and error correction\detection,and further proposes a generic optimization framework.This framework is capable of unifying the tasks of error detection and hierarchical error correction in each structure.In this way,the structures are adaptively assigned with different weights to adjust the contributions of them in representation procedure.Moreover,the introduction of the error correction mechanism suppresses the independent noises.The contributions of this thesis can be summarized as:1.This thesis proposes a novel matrix regression-based face recognition method to exploit the structured information on face in regression.And on this basis,the introduction of group-sparse regularizers takes full use of label information on training samples and further improve the robustness of proposed method.2.This thesis proposes a generic optimization framework of linear representation based on half-quadractial minimization and alternating direction method.This framework adjust the contributions of feature structures and suppresses the independent noises simultaneously in LR.3.The proposed framework is able to solve a combination of most popular estimation functions and regularizers with an acceptable convergence.In addition,this thesis conducts some experiments on series of public face database and validates the effectiveness and robustness of proposals.To further investigate proposed framework,this thesis also performs some experiments on non-facial databases which contain rich structured information.And the experimental results show the advantage of proposals for this type data.