Research On Sparse Representation Based Image Classification And Clustering Algorithms

With the rapid development of information technology,big data is profoundly changing people’s ways of thinking and life,and has promoted social progress and economic develop-ment.However,big data can also cause the problems of high complexity,excessive information,information redundancy,and so on.Therefore,how to effectively analyze data and learn robust and discriminative data representation is a very challenging problem.To solve this problem,sparse representation based feature learning algorithms have emerged.Sparse representation theory is a very important research topic in the field of pattern recognition.It has received close attention from many researchers in recent years due to its excellent data representation and feature extraction capabilities.From the perspective of whether the data are labelled or not,the existing sparse representation algorithms can be mainly divided into two categories:supervised and unsupervised,among which image classification based on supervised learning and image clustering based on unsupervised learning are the mainstream applications of sparse representation.In order to learn discriminative data representation and learn consistent features shared between different views,researchers have proposed many image classification and multi-view subspace clustering algorithms based on sparse representation.However,these algorithms still have the following problems:1 Thel₁/l₀-norm based sparse representation methods can-not effectively remove the large-area continuous block-occlusion noise in the face samples;2None of them have referred to the characteristics of deep learning to simultaneously explore the nonlinear and linear structures of data in the non-deep models;3 In the multi-view subspace clustering tasks,the impacts on the learning of common subspace caused by the views with fuzzy clustering structures cannot be adaptively weakened;4 Most of them assumed that the noise in samples only follows single kind of distribution which makes the model be not robust to the complex noise with mixed distributions;5 The design for structural representation learn-ing is unreasonable;6 The approach of learning the linear classifier and data representation in different regularization terms cannot guarantee that the learned representation is optimal for classification.In order to solve the above problems,this thesis mainly studies image classifica-tion and multi-view subspace clustering based on sparse representation,and proposes a series of improved algorithms.Specifically,the proposed algorithms can be generalized from three views:fixed dictionary,single synthesis dictionary learning,and dictionary pair learning.（1）Sparse representation based on fixed dictionary:1 In order to improve the robustness of thel₁-norm based sparse representation to continuous block-occlusion noise,we propose a nuclear-norm matrix regression based sparse-regularized face recognition algorithm.Related research shows that the continuous noise is usually low-rank.By minimizing the nuclear-norm of the two-dimensional error matrix,the low-rank structural information of the error can be fully utilized,so as to achieve the purpose of separating noise.Inspired by this,and simultaneously considering that the sparsity induced by thel₁-norm is conductive to enhancing the discrimi-native ability of data representation,this algorithm fuses the nuclear-norm based matrix regres-sion and thel₁-norm based sparse representation into a unified model which simultaneously explores the low-rank property of errors and the sparsity of representation.Experiments show that such a fusion can effectively alleviate the negative impact on face recognition caused by continuous block-occlusion noise.2 In order to inherit the merits of deep feature cascade and nonlinear feature transformation in deep learning,we propose a deep alternating cascaded rep-resentation learning algorithm.This algorithm alternately cascades the sparse and collaborative representations using the reconstruction error based Soft Max vectors,effectively integrating the sparsity and cooperativity of representation into a unified model.In addition,this algorithm can fully mine the potential discriminative structural information in the data,and can be regarded as the deep-layer extension of single-layer sparse coding model.Experiments show that with the increase of the number of cascaded layers,the classification accuracy of the proposed deep-layer representation learning model is significantly better than that of the traditional single-layer model.（2）Sparse representation based on single synthesis dictionary learning:3 In order to quickly and accurately cluster large-scale data,we propose a fast self-guided multi-view sub-space clustering algorithm.This algorithm takes the common anchor learning strategy as the research baseline.First,each local view is used to learn the consistent representation shared by different views in turn,and then uses the global features obtained by concatenating all views to learn the global data representation that contains all discriminative information.In order to connect global learning and local learning,this algorithm uses thel_2,1-norm to learn the row-sparse projection matrix so that the model can adaptively select the most useful features from the global discriminative information to guide the learning of local common subspace.Based on the global-supervise-local learning approach,this algorithm can effectively suppress those views with unclear cluster structures and redundant information when learning the local consis-tency representation.The experimental results show that the algorithm can achieve higher clus-tering accuracy and clustering efficiency than the latest anchor learning and deep learning based multi-view subspace clustering algorithms.4 In order to learn a more reasonable structured data representation and improve the robustness of dictionary learning to mixed-noise,we pro-pose a relaxed block-diagonal representation based noise-robust dictionary learning algorithm for face recognition.Based on the low-rank matrix recovery theory,this algorithm imposes both thel₁-norm and F-norm constraints on the reconstruction error of dictionary learning,so that the model can simultaneously remove the noises that follow the Laplacian and Gaussian distributions from contaminated samples.In addition,this algorithm class-wisely introduces thel_2,1-norm based relaxation term on the strict‘0-1’block-diagonal structure,which enables the model to learn the block-diagonal structure in a more relaxed way and to effectively preserve the similarity of intra-class representation.Experiments show that integrating relaxed block-diagonal representation learning and low-rank representation based mixed-noise removal can effectively improve the performance of face recognition under complex noise contamination.（3）Sparse representation based on dictionary pair learning:5 In order to simultaneously learn structured synthesis and analysis dictionaries,we propose a locality-constrained relaxed block-diagonal representation based dictionary pair learning algorithm.Based on the strict’0-1’block diagonal structure,this algorithm proposes an Hadamard-product based relaxed represen-tation learning term,which enables the model to more relaxedly and efficiently learn structured data representation and ensure the diversity of synthesis dictionary atoms.In addition,in order to avoid the process of representation learning being too relaxed,this algorithm introduces a locality-preservation term to encourage similar samples to have similar analytical codes.Ex-periments show that the relaxation learning term based on Hadamard product and the locality-preserving term for analytical coding are complementary and both of them help to improve the classification performance of the model.6 In order to learn a structured representation more suitable for classification,we propose a scale-constrained adaptive structured representation based dictionary pair learning algorithm.This algorithm first imposes the non-negative con-straint on the representation coefficients,and then uses the binary label matrix of dictionary atoms to linearly project the representation coefficients of the training samples into the corre-sponding binary label matrix of the training samples.In this way,this algorithm can adaptively learn a block-diagonal structured data representation with the scale constraint of’sum is 1’.Be-cause the label matrix of the dictionary can be directly used as a linear classifier,this algorithm can achieve the purposes of structured representation learning and linear classifier learning using only one regularization term,which significantly reduces the complexity of model optimization and parameter adjustment.Experiments show that this algorithm can achieve higher classifica-tion accuracy than the latest dictionary learning and even some deep learning algorithms.