| Dictionary learning has been widely applied in image processing,pattern recognition,machine vision and so on.Discriminative dictionary learning is an important research branch in the field of dictionary learning,and the core problem is to design discriminative terms for improving discriminative ability of the dictionary.In general,the methods based on discriminative terms can be divided into two categories.The first category combines the characteristics of training samples and coding coefficients.However,in practical applications,since the training samples often include noise and outliers,the methods may not obtain the true geometrical structure of the training samples.Thus,it may degrade the classification performance of the dictionary.The second category of methods exploits the incoherence of atoms.The incoherence of atoms can be adaptively updated,since the data may lie on the nonlinear manifold embedded in a very high-dimensional ambient space,and thus the classification performance will be degraded.Therefore,how to design a robust discriminative term is one of the key problems in dictionary learning.It is also the focus of this dissertation.In this dissertation,we establish some robust discriminative dictionary learning models by combining the atoms and row vectors of the coding coefficients matrix(profiles)along with atoms.In order to improve the discriminative ability of the dictionary,we construct the structural models of the atoms by using the Laplacian graph,followed by constructing a robust discriminative model.It not only inherits the geometrical structure of training samples,but also preserves the geometric structure and incoherence of atoms.Since there are one-to-one correspondence between the profiles and atoms,in order to improve the discriminative ability of the learned dictionary,we construct some discriminative terms based on the Fisher criterion and geometrical structure of the profiles.This research will overcome the limitation of pattern recognition based on discriminative dictionary learning algorithm,e.g.,low robustness,low adaptiveness and low discriminative ability.The main research points in this dissertation are summarized as follows.(1)We give the detailed description of the profiles in ideal dictionary learning model,which can make the definition of profiles more intuitive and easy to understand.Moreover,the relationships between the profiles and atoms are established in ideal dictionary learning model,and the similarity theorem between the profiles and atoms are given.In addition,in ideal model of dictionary learning,the relations among the training samples,dictionary,coding coefficients matrix and profiles matrix are also presented.And then,a method of adapative labels of atoms is proposed by using the profiles.Thus,the theorem and method can be used to design a robust discriminant term for improving the discriminative ability of the dictionary.(2)We propose an adaptive locality constrained dictionary learning algorithm(ALC-DL).In the ALC-DL algorithm,a Laplacian graph is constructed to reflect the geometrical structure of atoms.And then,we use the profiles to measure the similarity of atoms,and construct a locality constraint term by using the coding coefficient matrix and Laplacian graph of atoms.Since the profiles and atoms can be adaptively updated in the dictionary learning process,the locality constraint term has favorable robustness.Moreover,we establish relationships between the ALC-DL algorithm and some previous dictionary learning and sparse coding algorithms.Experimental results show that the proposed ALC-DL algorithm can achieve better classification performance than some state-of-the-art dictionary learning based on the locality constraint of the training samples.(3)Previous dictionary learning algorithms do not simultaneously take the locality and label information of atoms into account in the learning process,thus their performance is limited.In this dissertation,a discriminative dictionary learning algorithm,called the locality constrained and label embedding dictionary learning(LCLE-DL)algorithm,is proposed for image classification.Specifically,the LCLE-DL algorithm uses the specific class dictionary learning algorithms to assign the labels of the training samples to atoms.The label embedding term is constructed by using the label information of atoms,which encourages the atoms of the same class to have similar profiles.Then,we combine the label embedding and locality constraint of atoms to learn a dictionary by using two discriminative terms,it can ensure that the transformation between the label embedding and locality constraint is mutual.Thus,it can improve the robustness of discriminative terms.We utilize the 2l norm to ensure that the locality-based and label-based coding coefficients are as approximate to each other as possible,and it also can reduce the computational complexity.Moreover,we establish the relationships between the LCLE-DL algorithm and two dictionary learning algorithms based on the label information.Experimental results show that the LCLE-DL algorithm can achieve better classification performance in comparison with some state-of-the-art dictionary learning algorithms that use only the label or the locality constraint term.(4)We propose a discriminative dictionary learning algorithm based on the Fisher discriminative criterion and locality constraint of profiles(FDLC-DL).In the FDLC-DL algorithm,the Fisher discriminative criterion is imposed on the profiles so that they have small within-class compactness but large between-class separability.Since the profiles can be used to measure the similarity of atoms,the Fisher discriminative criterion of profiles can improve the discriminative ability of the learned dictionary.Moreover,existing dictionary learning algorithms do not consider the geometrical structure of the coding coefficients matrix in the learning process,which leads to limited performance.To this end,we construct the Laplacian graph of profiles to preserve the geometrical structure of the profiles matrix,and combine the atoms to construct a discriminative term.Since the profiles matrix is the transposed matrix of the coding coefficients matrix,the locality constraint on profiles also can improve the discriminative ability of the learned dictionary.Since the profiles and atoms can be adaptively updated,the discriminative terms of the FDLC-DL algorithm have good robustness.In order to reduce the computational complexity,we use the 2l norm to constrain the coding coefficients.Moreover,we establish the relationships between the FDLC-DL algorithm and other dictionary learning algorithms.Experimental results show that the proposed FDLC-DL algorithm can achieve better classification performance than some state-of-the-art dictionary learning and sparse coding algorithms.In summary,in order to improve robustness of discriminative terms of the dictionary learning algorithms,this dissertation puts forward three novel dictionary learning algorithms by using three different discriminative terms.Convincing experiments show that the proposed methods achieve promising classification performance. |
