权向量投影多平面支持向量机

Multisurface Support Vector Machines via Weight Vector Projection

提出一个多平面支持向量机算法——权向量多平面支持向量机(WMPSVM).该方法利用差代替Rayleigh商问题,从而避免广义特征值的奇异问题.与传统分类器不同,该方法无需求解具体的超平面,仅求解两个权向量.其决策是将测试样本归为距样本投影均值距离最近的所在的类.从广义支持向量机(GEPSVM)求解目的出发,该方法在保证得到与GEPSVM相当的计算效率的前提下,能较好地求解异或问题以及一些复杂异或问题.最后在人工数据集和UCI数据集上显示,该方法的性能要好于GEPSVM.

A multisurface support vector machine classifier is proposed called multisurface support vector machines via weight vector projection. It generates two weight vectors by solving two simple eigenvalue problems without consideration of the matrix singularity in it. Unlike the standard classifiers, the solution of the specific hyperplane is not required. According to the decision rule of the proposed approach, a unseen point is assigned to the closest projected mean. The proposed approach obtains comparable computational efficiency compared with proximal support vector machine via generalized eigenvalues （GEPSVM）. Moreover, it solves some complex XOR problems as well. The experimental results on artificial and UCI datasets show that the classification performance of the proposed approach outperforms that of GEPSVM.