Sparse Twin Support Vector Machines Based On Bilevel Programming

This paper mainly studies the Sparse Twin Support Vector Machines(TSVM)based on Bilevel Programming.Firstly,L_q(0?q<1)norm is combined with Least Squares TSVM(LSTSVM)to make it capable of feature selection and recognition at the same time.Then,combining the data sparse method based onL_q(0?q<1)norm with TSVM,a variety of Sparse TSVM based on Bilevel Programming are proposed.This paper mainly contains 5chapters.The first chapter mainly introduces the basic models and solving algorithms of TSVM,LSTSVM,Projection TSVM(LSPTSVM),Least Square Projection TSVM(LSPTSVM),Laplacian TSVM(Lap-TSVM),Laplacian LSTSVM(Lap-LSTSVM),Sparse Representation(SR)and Sparsity Preserving Projections(SPP).In the second chapter,three kinds of Least Squares forms of Sparse TSVM based onL_q(0?q<1)norm Sparse LSTSVM,Sparse LSPTSVM and Sparse Lap-LSTSVM are studied,and a series of comparative experiments are carried out on multiple image data sets to verify the effectiveness of the algorithms.In chapter 3,the sparse solving algorithm based onL_q(0?q<1)norm is integrated with TSVM,and the Sparse TSVM based on Bilevel Programming is proposed.Considering its Least Squares form and local structure information of data,the Least Squares Sparse TSVM and Laplacian Sparse TSVM are proposed respectively.In chapter 4,the Sparse Projection TSVM based on Bilevel Programming is proposed by combining sparse solving algorithm basedL_q(0?q<1)norm with the projection TSVM,and its least squares form is considered.In chapter 5,combining SPP with TSVM,a Sparsity Preserving Projections TSVM based on Bilevel Programming is proposed.Considering its least squares form and supervised sparse representation of data,the Least Square Sparsity Preserving Projections TSVM and Supervision Sparsity Projections TSVM are proposed respectively.