• 中国精品科技期刊
  • CCF推荐A类中文期刊
  • 计算领域高质量科技期刊T1类
Advanced Search
He Wenbin, Liu Qunfeng, Xiong Jinzhi. The Error Theory of Polynomial Smoothing Functions for Support Vector Machines[J]. Journal of Computer Research and Development, 2016, 53(7): 1576-1585. DOI: 10.7544/issn1000-1239.2016.20148462
Citation: He Wenbin, Liu Qunfeng, Xiong Jinzhi. The Error Theory of Polynomial Smoothing Functions for Support Vector Machines[J]. Journal of Computer Research and Development, 2016, 53(7): 1576-1585. DOI: 10.7544/issn1000-1239.2016.20148462

The Error Theory of Polynomial Smoothing Functions for Support Vector Machines

More Information
  • Published Date: June 30, 2016
  • Smoothing functions play an important role in the theory of smooth support vector machines. In 1996, Chen et al proposed a smoothing function of support vector machines—the integral function of Sigmoid function, and solved the error problem of the smoothing function. From 2005 to 2009, Yuan, Xiong and Liu proposed an infinite number of polynomial smoothing function and the corresponding reformulations for support vector machines. However, they did not touch the error functions for this class of polynomial smoothing functions. To fill up this gap, this paper studies the problem of the error functions with the Newton-Hermite interpolation method. The results show that: 1) the error functions of this class of polynomial smoothing functions can be calculated using the Newton-Hermite interpolation method, and the detailed algorithm is given; 2) there are an infinite number of error functions for this class of polynomial smoothing functions and a general formulation is obtained to describe these error functions; 3) there are several important properties for this class of error functions and the strict proof is given for these properties. By solving the problem of the error functions and their properties, this paper establishes an error theory of this class of polynomial smoothing functions, which is a basic theoretical support for smooth support vector machines.
  • Related Articles

    [1]Shen Jie, Long Biao, Jiang Hao, Huang Chun. Implementation and Optimization of Vector Trigonometric Functions on Phytium Processors[J]. Journal of Computer Research and Development, 2020, 57(12): 2610-2620. DOI: 10.7544/issn1000-1239.2020.20190721
    [2]Fu Liguo, Pang Janming, Wang Jun, Zhang Jiahao, Yue Feng. Optimization of Library Function Disposing in Dynamic Binary Translation[J]. Journal of Computer Research and Development, 2019, 56(8): 1783-1791. DOI: 10.7544/issn1000-1239.2019.20170871
    [3]Wang Ruiwei, Li Zhanshan, Li Hongbo. Optimizing eSTR Algorithm for Solving Constraint Satisfaction Problems[J]. Journal of Computer Research and Development, 2016, 53(7): 1586-1595. DOI: 10.7544/issn1000-1239.2016.20150284
    [4]Huang Guangqiu, Sun Siya, Lu Qiuqin. SEIRS Epidemic Model-Based Function Optimization Method—SEIRS Algorithm[J]. Journal of Computer Research and Development, 2014, 51(12): 2671-2687. DOI: 10.7544/issn1000-1239.2014.20130814
    [5]Feng Xiang, Ma Meiyi, and Yu Huiqun. Lake-Energy Optimization Algorithm for Travelling Salesman Problem[J]. Journal of Computer Research and Development, 2013, 50(9): 2015-2027.
    [6]Wu Jianhui, Zhang Jing, Li Renfa, Liu Zhaohua. A Multi-Subpopulation PSO Immune Algorithm and Its Application on Function Optimization[J]. Journal of Computer Research and Development, 2012, 49(9): 1883-1898.
    [7]Cai Shaobin, Gao Zhenguo, Pan Haiwei, Shi Ying. Localization Based on Particle Swarm Optimization with Penalty Function for Wireless Sensor Network[J]. Journal of Computer Research and Development, 2012, 49(6): 1228-1234.
    [8]Gong Wenyin and Cai Zhihua. Research on an ε-Domination Based Orthogonal Differential Evolution Algorithm for Multi-Objective Optimization[J]. Journal of Computer Research and Development, 2009, 46(4): 655-666.
    [9]Qi Yutao, Liu Fang, and Jiao Licheng. A Pheromone Meme Based Immune Clonal Selection Algorithm for Function Optimization[J]. Journal of Computer Research and Development, 2008, 45(6).
    [10]Hao Zhongxiao, Li Yanjuan. Study on Membership Problem with Respect to Temporal Functional Dependencies and Temporal Multivalued Dependencies[J]. Journal of Computer Research and Development, 2006, 43(7): 1267-1272.

Catalog

    Article views (1149) PDF downloads (468) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return