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Sparse kernel logistic regression based on L1/2 regularization

Science China(Information Sciences) 2013年第4期56卷 75-90页

作者： XU Chen PENG ZhiMing JING WenFeng Department of Statistics University of British ColumbiaVancouverBC V6T1Z2Canada Institute for Information and System Science School of Mathematics and StatisticsXi'an Jiaotong University

The sparsity driven classification technologies have attracted much attention in recent years,due to their capability of providing more compressive representations and clear *** most popular classification approaches are support vector machines(SVMs) and kernel logistic regression(KLR),each having its own *** sparsification of SVM has been well studied,and many sparse versions of 2-norm SVM,such as 1-norm SVM(1-SVM),have been ***,the sparsifiation of KLR has been less *** existing sparsification of KLR is mainly based on L1 norm and L2 norm penalties,which leads to the sparse versions that yield solutions not so sparse as it should be.A very recent study on L1/2 regularization theory in compressive sensing shows that L1/2 sparse modeling can yield solutions more sparse than those of 1 norm and 2 norm,and,furthermore,the model can be efficiently solved by a simple iterative thresholding *** objective function dealt with in L1/2 regularization theory is,however,of square form,the gradient of which is linear in its variables(such an objective function is the so-called linear gradient function).In this paper,through extending the linear gradient function of L1/2 regularization framework to the logistic function,we propose a novel sparse version of KLR,the 1/2 quasi-norm kernel logistic regression(1/2-KLR).The version integrates advantages of KLR and L1/2 regularization,and defines an efficient implementation scheme of sparse *** suggest a fast iterative thresholding algorithm for 1/2-KLR and prove its *** provide a series of simulations to demonstrate that 1/2-KLR can often obtain more sparse solutions than the existing sparsity driven versions of KLR,at the same or better accuracy *** conclusion is also true even in comparison with sparse SVMs(1-SVM and 2-SVM).We show an exclusive advantage of 1/2-KLR that the regularization parameter in the algorithm can be adaptively set whenever the sparsity(c

关键词： classification L1/2 regularization thresholding algorithm kernel logistic regression support vectors

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