改进向量投影的支持向量预选取方法

针对基于向量投影的支持向量预选取方法选取投影直线过于简单粗糙,导致需要选取较多的边界向量才能包含原始问题的支持向量的问题,提出了一种新的支持向量预选取方法.该方法通过定义好的投影直线具备的3个必要特征,提出:对于线性可分情况,利用Fisher线性判别算法来获取最佳的投影直线;对于非线性可分情况,利用特征空间中心向量所在直线作为相应的投影直线.由于该方法确定的投影直线可以更好地对样本投影进行分离,因此,与基于向量投影的支持向量预选取方法相比,该方法可用更少的原始样本来构造边界向量集合,可有效降低支持向量机算法的时空复杂度.在两个人工数据集和一个现实数据集上的实验表明,所提方法不仅可以达到以往各种实用的支持向量机算法分类精度,而且更为高效.

Support Vectors Pre-Extracting Method Based on Improved Vector Projection

For the question that the projection line of support vectors pre-extracting method based on vector projection is selected so rough that more bound vectors need to be selected to include the support vectors,a novel support vectors pre-extracting method is proposed.By defining the three necessary characteristics of a good projection line,for linear separable problems,the best projection orientation is determined by Fisher linear discriminant algorithm,and for non-linear separable problems,the orientation of the mean vector in the feature space is considered as the projection orientation.As the projection orientation determined by this method can separate the projection of the samples better,so compared with the previous support vectors pre-extracting method,the bound vectors set in this method can be composed of fewer original samples.Thus the time and space complexities of SVMs can effectively be reduced.Experiments on two artifical data sets and one real-world data set show that the proposed method can be as accurate as previous applied SVMs,but is much faster than them.