基于支撑向量机的收敛问题研究

Study on Metric Spaces Based on Support Vector Machine

在文章中提出了一种基于支持向量机思想的对任意距离空间求解最大分类间隔的方法，其优化问题可以用输入空间的距离来表示。首先将输入空间等距嵌入到Hilbert空间，在线性的Hilbert空间对优化问题进行线性处理，但是这种方法只适用于特定的距离空间。在原方案的基础上扩展研究了对任意距离空间求解最大分类间隔的方法。

This paper proposed a mammal margin classification method based on support vector machine （SVM） for arbitrary metric spaces. The optimization problem can be written in terms of the metric of the input space. Firstly we isometrically embedded the input space into a Hilbert space where we can solve the problem with linear method. However, this method is limited to special metric spaces. According to the scheme developed for SVM we provide a generalization of maximum margin principle to arbitrary metric space.