Abstract In this paper, the property is used that any matrices can be decomposed into symmetric positive semi-definite ones using extremum decomposition. It is used on RBF kernel to generate a new kernel, called Ked. Combining Ked with global poly kernel, a mixed kernel with good classification performance is constructed. The classification experiments on UCI database are deployed with the mixed kernel. Compared with RBF kernel, the experimental results show that mixed kernel can decrease the number of support vectors and has better classification performance. Furthermore, it has good training time when the value of RBF kernel parameter is small.
[1] Duda R, Hart P. Pattern Classification and Scene Analysis. New York, USA: Wiley, 1973 [2] Deng Naiyang, Tian Yingjie. The New Data Mining Method-Support Vector Machines. Beijing, China: Science Press, 2004 (in Chinese) (邓乃扬,田英杰.数据挖掘中的新方法——支持向量机.北京:科学出版社, 2004) [3] Amari S, Wu S. Improving Support Vector Machine Classifiers by Modifying Kernel Functions. Neural Networks, 1999, 12(6): 783-789 [4] Haussler D. Convolution Kernels on Discrete Structures. Technical Report, UCSC-CRL-99-10, Santa Cruz, USA: University of California Santa Cruz, 1999 [5] Zhang Sheng, Liu Jian, Tian Jinwen. An SVM-Based Small Target Segmentation and Clustering Approach // Proc of the 3rd International Conference on Machine Learning and Cybernetics. Shanghai, China, 2004: 3318-3323 [6] Ye Ning, Sun Ruixiang, Liu Yingan. Support Vector Machine with Orthogonal Chebyshev Kernel // Proc of the 18th International Conference on Pattern Recognition. Hongkong, China, 2006, Ⅱ: 752-755 [7] Zhu Yanfei, Wu Jianping, Li Qi, et al. Modeling of LS-SVM Based on Mixtures of Kernels for MISO Systems. Control and Decision, 2005, 20(4): 417-420 (in Chinese) (朱燕飞,伍建平,李 琦,等.M ISO系统的混合核函数LS-SVM建模.控制与决策, 2005, 20(4): 417-420) [8] Liu Xiangdong, Lou Bin, Chen Zhaoqian. Optimal Model Selection for Support Vector Machines. Journal of Computer Research and Development, 2005, 42(4): 576-581 (in Chinese) (刘向东,骆 斌,陈兆乾.支持向量机最优模型选择的研究.计算机研究与发展, 2005, 42(4): 576-581) [9] Hong Ziquan, Yang Jingyu. Image Algebraic Feature Extraction for Image Recognition. Pattern Recognition, 1991, 24(3): 211-219 [10] Lu Yang, Wang Haiyan, Tian Na. A Support Vector Machine with a Hybrid Kernel and Its Application in Underwater Target Recognition. Technical Acoustics, 2005, 24(3): 144- 147 (in Chinese) (陆 阳,王海燕,田 娜.组合核函数支持向量机在水中目标识别中的应用.声学技术, 2005, 24(3): 144-147) [11] Shi Zhongzhi. Knowledge Discovery. Beijing, China: Tsinghua University Press, 2002 (in Chinese) (史忠植.知识发现.北京:清华大学出版社, 2002) [12] Kong Yue, Shi Zesheng, Guo Li, et al. Improving Performance of Kernel Principal Component Analysis Using Combination Kernel Functions. Journal of Image and Graphics, 2004, 9(1): 40-45 (in Chinese) (孔 锐,施泽生,郭 立,等.利用组合核函数提高核主分量分析的性能.中国图象图形学报, 2004, 9(1), 40-45) [13] Kernel-Machines.Org.SVM-QP [DB/OL]. [2008-01-20]. http://www.kernel-machines.org/sofware
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