Projection multi-birth support vector machinea for multi-classification

摘要

As an important multi-classification learning tool, multi-birth support vector machine (MBSVM) has been widely studied and applied due to its low computational complexity and good generalization. In this paper, a new multi-birth support vector machine is proposed to handle multi-class classification problem, called projection multi-birth support vector machine (PMBSVM). Specifically, we intend to seek a projection direction wk for k-th class, so that the covariance of remaining samples (except the k-th class) is as small as possible, and the samples of k-th class are as far as possible from the mean of the remaining samples. The proposed PMBSVM not only inherits the advantages of MBSVM, but also can find a suitable projection direction for each class so that the sample is separable in the projection space. Additionally, a regularization term is introduced to maximize the margin of different classes in the projected space. Moreover, a recursive PMBSVM algorithm is proposed for generating multiple orthogonal projection directions for each class. Then we extend the proposed approaches to nonlinear situations through kernel technology. Simulation results on benchmark datasets show that the proposed algorithms improve the generalization in most cases.