经典线性算法的非线性核形式

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．

Nonlinear Kernel Forms of Classical Linear Algorithms

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.