|
|
Multisurface Support Vector Machines via Weight Vector Projection |
YE Qiao-Lin ,YE Ning,CUI Jing,CHEN Yan-Nan,WU Bo |
School of Information Technology,Nanjing Forestry University,Nanjing 210037 |
|
|
Abstract A multisurface support vector machine classifier is proposed called multisurface support vector machines via weight vector projection. It generates two weight vectors by solving two simple eigenvalue problems without consideration of the matrix singularity in it. Unlike the standard classifiers, the solution of the specific hyperplane is not required. According to the decision rule of the proposed approach, a unseen point is assigned to the closest projected mean. The proposed approach obtains comparable computational efficiency compared with proximal support vector machine via generalized eigenvalues (GEPSVM). Moreover, it solves some complex XOR problems as well. The experimental results on artificial and UCI datasets show that the classification performance of the proposed approach outperforms that of GEPSVM.
|
Received: 05 January 2009
|
|
|
|
|
[1] Vapnik V N. Statistical Learning Theory. New York, USA: John Wiley, 1998 [2] Mangasarian O L, Wild E W. Multisurface Proximal Support Vector Machine Classification via Generalized Eigenvalues. IEEE Trans on Pattern Analysis and Machine Intelligence, 2006, 28(1): 69-74 [3] Yang Xubing, Chen Songcan. Proximal Support Vector Machine Based on Prototypal Muticlassification Hyperplanes. Journal of Computer Research and Development, 2006, 43(10): 1700-1705 (in Chinese) (杨绪兵,陈松灿.基于原型超平面的多类最接近支持向量机.计算机研究与发展, 2006, 43(10): 1700-1705) [4] Yang Xubing, Chen Songcan, Yang Yimin. Localized Proximal Support Vector Machine via Generalized Eigenvalues. Chinese Journal of Computers, 2007, 30(8): 1227-1234 (in Chinese) (杨绪兵,陈松灿,杨益民.局部化的广义特征值最接近支持向量机.计算机学报, 2007, 30(8): 1227-1234) [5] Lee Y J, Mangasarian O L. RSVM: Reduced Support Vector Machines // Proc of the 1st SIAM International Conference on Data Mining. Chicago, USA, 2001: 5-7 [6] Richard D, Peter H. Pattern Classification and Scene Analysis. New York, USA: Wiley, 1973 [7] Su Yucai, Jiang Cuibo, Zhang Yuehui. Matrix Theory. Beijing, China: Science Press, 2006 (in Chinese) (苏育才,姜翠波,张跃辉.矩阵理论.北京:科学出版社, 2006) [8] Mika S, Ratsch G, Weston J, et al. Fisher Discriminant Analysis with Kernels // Proc of the IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing. Madison, USA, 1999: 41-48 [9] Muphy P M, Aha D W. UCI Repository of Machine Learning Databases [DB/OL]. [2009-01-01]. http://archive.ics.uci.edu/ml/ [10] Mitchell T M. Machine Learning. Boston, USA: McGraw-Hill, 1997 [11] Golub G H, Loan C F V. Matrix Computations. 3rd Edition. Baltimore, USA: John Hopkins University Press, 1996 [12] Kojima M, Mizuno S, Noma T, et al. A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. Berlin, Germany: Springer-Verlag, 1991 |
|
|
|