基于最小二乘支持向量机的函数型数据回归分析

摘要

Partial functional linear model is used to explore the relationship between the mixed_type input containing a functional variable and a numerical vector and a numerical output. To improve the accuracy of prediction, based on the representation of the functional coefficient in reproducing kernel Hilbert space, the structured representation of the model is obtained. The estimation problem of the functional coefficient is converted into the estimation problem of a parameter vector, and the least squares support vector machine method is used for parameter estimation. Experimental results show that the performance of vector coefficient estimator is similar to other parameter estimation methods while the functional coefficient estimator is stabler and more accurate than the others, and the good performance of the proposed method further ensures the accuracy of machine learning.%部分函数线性模型是用于处理输入变量包含函数型和数值型两种数据类型而输出变量为数值的一类回归机。为提高该模型的预测精度，基于函数系数在再生核Hilbert空间上的表示，得到模型的结构化表示，将函数系数的估计转化为参数向量的估计问题，并运用最小二乘支持向量机方法得到参数估计形式。实验表明，文中算法对数值型数据的向量系数的估计与其他参数估计方法性能相近，但对函数型数据的函数系数的估计更加准确稳健，有助于确保学习机的预测精度。