基于特征值分解的中心支持向量机算法

针对广义特征值中心支持向量机(GEPSVM)训练和决策过程不一致问题，该文提出一类改进的基于特征值分解的中心支持向量机，简称为IGEPSVM。首先针对二分类问题提出了基于特征值分解的中心支持向量机，然后基于一类对余类策略将其推广到多类分类问题。将GEPSVM求解广义特征值问题转化为求解标准特征值问题，降低了计算复杂度。引入了一个新的参数，可以调节模型的性能，提高了GEPSVM的分类精度。提出了基于IGEPSVM的多类分类算法。实验结果表明，与GEPSVM算法相比较，IGEPSVM不仅提高了分类精度，而且缩短了训练时间。

Eigenvalue Proximal Support Vector Machine Algorithm Based on Eigenvalue Decoposition

To deal with the consistency problem of training process and decision process in Generalized Eigenvalue Proximal Support Vector Machine (GEPSVM), an improved version of eigenvalue proximal support vector machine, called IGEPSVM for short is proposed. At first, IGEPSVM for binary classification problem is proposed, and then Multi-IGEPSVM is also presented for multi-class classification problem based on one-versus-rest strategy. The main contributions of this paper are as follows. The generalized eigenvalue decomposition problems are replaced by the standard eigenvalue decomposition problems, leading to simpler optimization problems. An extra parameter is introduced, which can adjust the performance of the model and improve the classification accuracy of GEPSVM. A corresponding multi-class classification algorithm is proposed, which is not studied in GEPSVM. Experimental results on several datasets illustrate that IGEPSVM is superior to GEPSVM in both classification accuracy and training speed.