基于最小闭球的多类支持向量机

针对多类分类问题中样本数量分布不均衡和测试速度较慢两种情况，本文提出了两个基于闭球的二叉树多类支持向量机算法：MEB-MCSVM-1和MEB—MCSVM-2．算法利用最小闭球来协调样本数量间的不均衡性，利用球心进行最远距离聚类或最近-最远距离聚类，构建二叉树结构，使二又树的每个节点代表】个二类支持向量机．为了检验所提算法的有效性，本文从需要训练的SVM个数、训练时间和测试时间三个方面对五种算法1-v-1，1-v-r，MEB-MCS—VM-0，MEB-MCSVM-1和MEB—MCSVM-2进行了比较分析，结果表明本文所提方法对解决多类分类问题中样本数目不均匀和测试速度较慢这两种情况有明显的优势，实用性更强．

Multi-class SVMs Based on Minimum Enclosing Balls

In this paper, two binary-tree multi-class SVM algorithms based on enclosing balls, MEB-MCSVM-1 and MEB-MCSVM-2, are presented for solving the imbalance of sample distribution and slowly testing speed in multi-class classification problems. They can adjust the imbalance of sample distribution between two classes by using minimum enclosing balls and can cluster by using maximum distance or minimum-maximum distance of centres of balls. Then they can construct binary-tree struc- tures such that a binary SVM can be used at each node of binary-tree structures. In order to verity the performance of the algorithms presented in this paper, comparative analysis with algorithms 1-v-l, 1-v-r, MEB-MCSVM-0, MEB-MCSVM-1 and MEB-MCSVM-2 is performed from the three aspects of the de- manding number of SVMs, the training time and the testing time. The results show that our methods have obvious advantage and are more practical.