Through releasing the equal-margin constraint in the standard support vector machines (SVM), keeping the sum of the binary-class function margins, a new SVM was gotten within the framework of SVM. The separating hyperplane of the new SVM can be adjusted as per the distribution of the binary-class samples, and its dual express is same as the standard SVM. Thus, the SVM was further improved theoretically. On the basis of the new SVM, a concrete algorithm, variance modification algorithm, was proposed. In the variance modification algorithm, the binary-class margins are in proportion to the standard deviation of binary-class samples. The goal of adjusting the optimal separating hyperplane as per sample-s variance is attained through the variance modification algorithm. Statistically, errors are reduced through the variance modification algorithm, while the computational complexity is not increased much.
������,��ѧ��.ģʽʶ��[M].����:�廪��ѧ������,2000 Bian Zhaoqi, Zhang Xuegong. Pattern recognition [M]. Beijing: Tsinghua University Press, 2000 (in Chinese)
Gert R G Lanckriet, Laurent El Ghaoui, Chiranjib Bhattacharyya, et al.A robust minimax approach to classification[J].Journal of Machine Learning Research.2002, 3:555-582
Huang Kaizhu, Yang Haiqin, King Irwin, et al.Maxi-min margin machine: learning large margin classifiers locally and globally[J].IEEE Transactions on Neural Networks.2008,19(2):260-272
Wang Defeng, Yeung D S, Tsang E C C. Probabilistic large margin machine Proceeding of the Fifth International Conference on Machine learning and Cybernetics. Dalian: , 2006: 2190-2195
Nello Cristianini, John Shawe-Taylor.֧������������[M]. �����,����,������,��.����:���ӹ�ҵ������,2004 Nello Cristianini, John Shawe-Taylor. An introduction to support vector machines and other kernel-based learning methods[M]. Translated by Li Guozheng, Wang Meng, Zeng Huajun. Beijing: Publishing House of Electronic Industry, 2004(in Chinese)
Vladimir N Vapnik. An overview of statistical learning theory[J].IEEE Transactions on Neural Networks.1999, 10(5):988-999
�Ĵ���,ղ����. �����Ե��ڷ�����SVM ��ƽ�ⲻƽ�����ݷ���[J]. ϵͳ����, 2009,27(3):110��114 Wen Chuanjun, Zhan Yongzhao. Balance and imbalance data set classification based on self-adjusting classification-plane SVM[J]. Systems Engineering, 2009, 27(3):110-114(in Chinese)