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经典线性算法的非线性核形式
引用本文:许建华,张学工. 经典线性算法的非线性核形式[J]. 控制与决策, 2006, 21(1): 1-0006
作者姓名:许建华  张学工
作者单位:南京师范大学,数学与计算机学院,南京,210097;清华大学,自动化系,北京,100084
基金项目:国家自然科学基金项目(60275007);江苏省自然科学基金项目(BK2004142).致谢非常感谢清华大学自动系李衍达教授、阎平凡教授和陆文凯副教授对本项研究工作的指导和大力支持.
摘    要:经典线性算法的非线性核形式是近10年发展起来的一类非线性机器学习技术.它们最显著的特点是利用满足Mercer条件的核函数巧妙地推导出线性算法的非线性形式。并表述为与样本数目有关、与维数无关的优化问题.为了提高数值计算的稳定性、控制算法的推广能力以及改善迭代过程的收敛性。部分算法还采用了正则化技术.在概述核思想与核函数、正则化技术的基础上,系统地介绍了经典线性算法的非线性核形式,同时分析它们的优缺点,井讨论了进一步发展的方向.

关 键 词:机器学习  核函数  核形式  支持向量机
文章编号:1001-0920(2006)01-0001-06
收稿时间:2004-12-15
修稿时间:2004-12-152005-04-18

Nonlinear Kernel Forms of Classical Linear Algorithms
XU Jian-hua,ZHANG Xue-gong. Nonlinear Kernel Forms of Classical Linear Algorithms[J]. Control and Decision, 2006, 21(1): 1-0006
Authors:XU Jian-hua  ZHANG Xue-gong
Affiliation:1. School of Mathematical and Computer Sciences, Nanjing Normal University, Nanjing 210097, China; 2. Department of Automation, Tsinghua University, Beijing 100084, China.
Abstract:In machine learning the nonlinear kernel forms of classical linear algorithms are a class of nonlinear techniques developed in the last ten years. The most attractive idea is that by using kernel functions satisfying Mercer condition the classical linear algorithms are skillfully extended to construct their nonlinear kernel forms. These nonlinear algorithms are described by optimization problems that depend on the size of training sets rather than the dimension of sample vectors. In order to improve numerical stability, control generalization ability and improve convergence of iterative procedures, the regularization technique is utilized in some algorithms. On the basis of summarizing the kernel idea and kernel functions and regularization technique, the nonlinear kernel forms of linear algorithms are surveyed. Related properties are disscussed and further research directions are pointed out.
Keywords:Machine learning   Kernel function   Kernel forms   Support vector machine
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