Feature Extraction Algorithms Based On Graph Embedding And Elastic Net Regression With Applications To Face Recognition

In the procedure of face recognition,the focus of feature extraction is to dig and extract the effective features in the face data,which is conducive to improve the ability of classification and identification of the algorithms.The traditional feature extraction algorithms based on Subspace Learning such as Principal Component Analysis(PCA)and Linear Discriminant Analysis(LDA),and Graph Embedding feature extraction algorithms based on Manifold Learning such as Locally Linear Embedding(LLE)and Local Preserving Projection(LPP)are widely used because of the advantages of simpleness,intuitive and high efficiency.However,the algorithms mentioned above still have many problems and limitations,for example,the global and local structures of data cannot be obtained at the same time,linear methods are not ideal for nonlinear data processing,the problem of “Small Sample Size” and feature redundancy.The research based on sparse feature extraction is another hot spot in face recognition field.The original face data often contains many features,sparse feature extraction can find some of the most significant features from the original data,then use them to make up a minimum feature subset to represent the original data optimally,this process can both simplify the data and preserve the key information in the data.Elastic Net regression is one of the commonly used sparse feature extraction algorithms.This paper combines the commonly used graph embedding algorithms with Elastic Net regression to study the above-mentioned problems existing in feature extraction algorithms and propose new algorithms,then apply them in face recognition.The main work is as follows:(1)The simple introduction of face recognition,contains research background,development course,research contents and applications,existing problems.Then some typical face databases are simply introduced too.(2)According to the contents of this paper,the thoughts of Graph Embedding based on Manifold Learning and sparse feature extraction are introduced respectively.And the implementation steps of classic feature extraction algorithms(PCA,LDA,LLE and LPP)and sparse feature extraction algorithms(Ridge regression,Lasso regression and Elastic Net regression)are introduced in detail,then the advantages and disadvantages of the above-mentioned algorithms are simply analyzed.(3)Combined PCA,LLE with Elastic Net regression,the feature extraction algorithm named Unsupervised Sparse Difference Embedding(USDE)was proposed.The basic idea of this algorithm is: Firstly,constructing LLE-based “local minimum embedding” and PCA-based “global maximum variance”;secondly,using the form of “difference” to solve the multi-objective optimization problem with a sparsity constraint to construct the objective function of USDE;finally,using the Elastic Net regression to achieve the sparsity.(4)Based on Maximum Margin Criterion(MMC),Combined LLE with Elastic Net regression,the feature extraction algorithm named Sparse Local Embedding based on Maximum Margin Criterion(SLE/MMC)was proposed.Firstly,SLE/MMC constructs intra-class scatter matrix and inter-scatter matrix on the basis of preserving local neighborhood;and secondly SLE/MMC uses the form of “MMC” and a sparsity constraint to construct the objective function of SLE/MMC;finally,SLE/MMC uses the Elastic Net regression to obtain a sparse result.(5)Combined Two-Dimensional Discriminant Local Preserving Projection(2DDLPP)with Elastic Net regression,the feature extraction algorithm named Sparse Two-Dimensional Discriminant Local Preserving Projection(S2DDLPP)was proposed.2DDLPP introduced between-class scatter and label information into LPP,and directly use the image matrix instead of the vector for feature mapping,which can reduce the loss of information in the transformation process.Firstly,based on 2DDLPP,S2 DDLPP combines sparse constraints to its objective function while “minimizing intra-class distance” and “maximizing inter-class distance”;and secondly,S2 DDLPP uses Elastic Net regression to achieve the sparsity,and an optimal sparse projection matrix is obtained.