支持向量预选的凸壳顶点法

为减少参训样本数量,加快支持向量机在大规模数据集上的学习速度,提出一种基于凸壳顶点法的支持向量预选算法.该算法基于线性可分样本集凸壳顶点的集合必然是支持向量超集的事实,运用对偶原理将凸壳顶点的求解转化为判断线性规划是否有解,从而求出样本集的凸壳顶点.构造了非线性映射函数,并将该算法推广到非线性可分样本集.基于人工数据集和标准数据集的实验结果验证了算法的有效性.

Preselecting support vectors by convex hull vertex method

To reduce the size of samples in training and accelerate the learning speed of support vector machine on large
scale datasets, an approach for preselecting support vectors by convex hull vertex method is proposed. Based on the fact
that the superset of support vectors could be formed by the convex hull vertexes of a linearly separating dataset, the duality
principle is applied to transform the solving of convex hull vertexes into the feasibility deciding of linear programmings.
Hence, all convex hull vertexes are accessible. Nonlinear mapping function is constructed to generalize the approach to
nonlinearly separating datasets. Experimental results on synthetic datasets and benchmark datasets show the effectiveness of
the proposed method.