Sparse Multinomial Logistic Regression Algorithm Based on Centered Alignment Multiple Kernels Learning

Abstract

As a generalized linear model, Sparse Multinomial Logistic Regression (SMLR) is widely used in various multi-class task scenarios. SMLR introduces Laplace priori into Multinomial Logistic Regression (MLR) to make its solution sparse, which allows the classifier to embed feature selection in the process of classification. In order to solve the problem of non-linear data classification, Kernel Sparse Multinomial Logistic Regression (KSMLR) is obtained by kernel trick. KSMLR can map nonlinear feature data into high-dimensional and even infinite-dimensional feature spaces through kernel functions, so that its features can be fully expressed and eventually classified effectively. In addition, the multi-kernel learning algorithm based on centered alignment is used to map the data in different dimensions through different kernel functions. Then center-aligned similarity can be used to select flexibly multi-kernel learning weight coefficients, so that the classifier has better generalization ability. The experimental results show that the sparse multinomial logistic regression algorithm based on center-aligned multi-kernel learning is superior to the conventional classification algorithm in classification accuracy.