Many kemelized classification methods, such as SVM and SVDD, are formulated as quadratic programming (QP) problems, but computing kernel matrix would require O( m2) computation, and solving QP may take up to O(m3), which limits these methods to train on large datasets. In this paper,a new classification method called Maximum Vector-Angular Margin Classifier (MAMC) is proposed,based on a new concept of margin called vector-angular margin,to find an optimal vector c in pattens＇feature space and all the testing points can be classified in terms of the maximum vector-angular margin p between the vector c and all the training points. Meanwhile, the kernelized MAMC can be equivalently formulated as the kernelized Minimum Enclosing Ball (MEB),and thus MAMC can be extended to Maximum Vector-Angular Margin Core Vector Machine (MAM-CVM) by introducing Core Vector Machine (CVM) method,to solve the training and classification for large datasets. Experimental results on artificial and real datasets are provided to validate the effectiveness of the proposed methods here.%许多核化形式的分类方法如SVM,SVDD等都是对应一个二次规划(QP)问题,而核矩阵计算需要0(m2)空间复杂度,求解QP需要0(m3)时间复杂度,限制了这类方法对大样本数据的训练.本文基于一种新的分类间隔概念提出最大向量夹角间隔分类器MAMC,目标是在样本空间找到最优向量c,测试样本通过c与训练样本之间的最大化向量夹角间隔p(称为Margin)实现分类.同时,文中证明了该方法的核化形式等价于核化的最小包络球MEB问题,并通过引入核心集向量机CVM将MAMC扩展为MAM-CVM,进而快速实现对大样本的训练和分类.人造和真实数据集实验表明了MAMC和MAM-CVM算法的有效性.
展开▼
