Semi-Supervised Proximal Support Vector Machine via Generalized Eigenvalues
YANG Xu-Bing1,2, PAN Zhi-Song3, CHEN Song-Can1
1.College of Information Science and Technology, Nanjing University of Aeronautics and Astronautics,Nanjing 210016 2.College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037 3.Institute of Command Automation, PLA University of Science Technology, Nanjing 210007
Abstract A binary classifier, proximal support vector machine via generalized eigenvalues (GEPSVM), has been proposed recently. In this paper, with the characteristics of plane classifiers and manifold learning, an effective semi-supervised algorithm SemiGEPSVM is proposed. It keeps the performance of handling XOR problems and is suitable for more challenges, even with only one labeled sample per class. While the number of labeled samples is not satisfactory to generate plane, k-nearest neighbor is used to select the unlabelled samples. Otherwise, the proposed sample selection method with plane characteristics is adopted. Furthermore, it is proved that the proposed selection method is global optimization. And the experimental results of SemiGEPSVM are verified on one toy problem and some benchmark datasets.
[1] Fung G, Mangasarian O L. Proximal Support Vector Machine Classifiers // Proc of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. San Francisco, USA, 2001: 77-86 [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] Jayadeva, Khemchandai R, Chandra S. Fuzzy Proximal Support Vector Classification via Generalized Eigenvalues // Proc of the 1st International Conference on Pattern Recognition and Machine Intelligence. Kolkata, India, 2005: 360-363 [4] Jayadeva, Khemchandai R, Chandra S. Fuzzy Multi-Category Proximal Support Vector Classification via Generalized Eigenvalues. Soft Computing-A Fusion of Foundations, Methodologies and Applications, 2007, 11(7): 679-685 [5] Jayadeva, Khemchandai R, Chandra S. Twin Support Vector Machines for Pattern Classification. IEEE Trans on Pattern Analysis and Machine Intelligence, 2007, 29(5): 905-910 [6] Li Haifeng, Jiang Tao, Zhang Keshu. Efficient and Robust Feature Extraction by Maximum Margin Criterion. IEEE Trans on Neural Networks, 2006, 17(1): 157-165 [7] Yang Xubing, Chen Songcan. Proximal Support Vector Machine Based on Prototypal Multiclassification 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) [8] Zhou Zhihua, Zhan Dechuan, Yang Qiang. Semi-Supervised Learning with Very Few Labeled Training Examples // Proc of the 22nd AAAI Conference on Artificial Intelligence. Vancouver, Canada, 2007: 675-680 [9] Zhou Dengyong, Weston J, Gretton A. Ranking on Data Manifolds // Thrun S, Saul L K, Schlkopf B, eds. Advances in Neural Information Processing Systems. Cambridge, USA: MIT Paress, 2004, 16: 169-176 [10] Zhang Dengyong, Zhou Zhihua, Chen Songcan. Semi-Supervised Dimensionality Reduction // Proc of the 7th SIAM International Conference on Data Mining. Minneapolis, USA, 2007: 629-634 [11] Bradley P S, Mangasarian O L. k-Plane Clustering. Journal of Global Optimization, 2000, 16(1): 23-32
2009, Vol. 22 
