最小平方误差算法的正则化核形式

最小平方误差算法是最常用的一种经典模式识别和回归分析方法,其目标是使线性函 数输出与期望输出的误差平方和为最小.该文应用满足Meteer条件的核函数和正则化技术,改 造经典的最小平方误差算法,提出了基于核函数和正则化技术的非线性最小平方误差算法,即 最小平方误差算法的正则化核形式,其目标函数包含基于核的非线性函数的输出与期望输出的 误差平方和,及一个适当的正则项.正则化技术可以处理病态问题,同时可以减小解空间和控制 解的推广性,文中采用了三种平方型的正则项,并且根据正则项的概率解释,详细比较了三种正 则项之间的差别.最后,用仿真资料和实际资料进一步分析算法的性能.

Regularized Kernel Forms of Minimum Squared Error Methods

Minimum squared error algorithm is one of the classical pattern recognition and regression analysis methods, whose objective is to minimize the squared error summation between the output of linear function and the desired output. In this paper, the minimum squared error algorithm is modified by using kernel functions satisfying Mercer condition and regularization technique, and a nonlinear minimum squared error algorithm based on kernels and regularization technique, i.e., the regularized kernel form of minimum squared error algorithms is proposed. Its objective function includes squared error summation between the output of nonlinear function based on kernels and the desired output, and a proper regularization term. The regularization technique can handle ill-posed problems, reduce the solution space and control the generalization. Three regularization terms of square form are utilized in this paper. According to the probabilistic interpretation of regularization terms, the difference among three regulari2ation terms is given in detail. The synthetic and real data are used to analyze the algorithm performance.