基于梯度信息的最小二乘支持向量回归机  

Improving LSSVR with Gradients/Derivatives

作　　者：蒋婷[1] 周晓剑[2] 

机构地区：[1]南京大学信息管理学院,江苏南京210093 [2]南京邮电大学管理学院,江苏南京210023

出　　处：《系统工程》2016年第1期127-133,共7页Systems Engineering

基　　金：2014年度全国统计科学研究重点项目(2014LZ42);教育厅哲社重点研究基地培育点招标课题(TJS211021)

摘　　要：经典的最小二乘支持向量回归机是基于样本点来构建模型,没考虑样本点处的梯度信息。如果样本信息容易获得,则可将其用于构建回归模型。有学者提出了一种基于梯度信息的构建方法,但其构建是基于泰勒展开,简单地将梯度信息插入到泰勒展开式中,并需要人为地去设定邻域的大小。本文另辟蹊径,将梯度信息作为第二类变量融入到核矩阵中直接构建优化模型,使模型的构建更为简捷直观,并据此得到一种新的基于梯度信息的最小二乘支持向量回归机模型。所提模型通过了一个二维函数的验证,实验表明,与传统的最小二乘支持向量回归机相比,考虑梯度信息的最小二乘支持向量回归机模型显著地提高了其预测精度。The classical least square support vector regression（LSSVR）focuses on the exact response values rather than the gradient information.Nevertheless,if the gradient/derivative information of the samples can be easily or cheaply obtained,we can utilize the gradients/derivatives to construct the regression model.The existing research proposed by Xiaojian Zhou et al,which is based on constructing of LSSVR with gradient information,carries out just from the perspective of Taylor expansion,simply inserting the additional objective values in the neighborhood of the sampled points into the corresponding terms of a Taylor expansion.But this technique requires defining the radius of the neighborhood.This research adopts another way to construct the optimization model by regarding the gradients as the second type variables rather than by estimating the function value in the neighborhood of the samples,making the model more simple and intuitional.This method is named as gradient-enhanced least square support vector regression（GELSSVR）.The efficiencies of this model are verified by a two-dimensional analytical function.The experimental results indicate that compared with LSSVR,GELSSVR greatly enhances its prediction precision.

关 键 词：最小二乘支持向量回归机 元模型 梯度信息 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]