超球体多类支持向量机理论

Theory of hypersphere multiclass SVM

目前的多类分类器大多是经二分类器组合而成的,存在训练速度较慢的问题,在分类类别多的时候,会遇到很大困难,超球体多类支持向量机将超球体单类支持向量机扩展到多类问题,由于每类样本只参与一个超球体支持向量机的训练,因此,这是一种直接多类分类器,训练效率明显提高.为了有效训练超球体多类支持向量机,利用SMO算法思想,提出了超球体支持向量机的快速训练算法.同时对超球体多类支持向量机的推广能力进行了理论上的估计.数值实验表明,在分类类别较多的情况,这种分类器的训练速度有很大提高,非常适合解决类别数较多的分类问题.超球体多类支持向量机为研究快速直接多类分类器提供了新的思路.

Constructed by standard binary classes support vector machine（SVM）, present multiclass SVMs are usually very slow to be trained. When a large number of categories of data are to be classified, the training work could be very difficult. By extending the hypersphere one-class SVM（HSOC-SVM） to a hypersphere multiclass SVM（HSMC-SVM）, we build a fast training classifier HSOC-SVM. Its training speed is higher than that of the present multiclass classifiers, because each category data trains only one HSOC-SVM. In order to improve the training speed for the HSMC-SVM,.we propose a training algorithm based on the existing algorithm for SMO. Meanwhile, the theoretic upper bound of the generalized error of HSMC-SVM is analyzed for evaluating the general performance of HSMC-SVM. Numeric experiments show that the training speed of HSMC-SVM is especially improved when many categories of data are to be classified. Thus, HSMC-SVM provides a new idea for developing fast-directed multiclass classifiers in machine learning area.