基于MATLAB的SVR回归模型的设计与实现
The Design and Implementation of SVR Regression Model
Based on MATLAB
摘 要
支持向量机是根据统计学习理论提出的一种新的学习方法，近年来受到了国内外学术界的广泛重视，并已在模式识别和函数估计中得到广泛应用。支持向量机理论的最大特点是由有限的训练集样本得到的小的误差保证对独立的测试集仍保持小的误差。从而通过支持向量机(SVM)理论,可以建立支持向量回归(SVR)预测模型，以解决各种实际问题。
SVR算法是模式识别中应用比较广泛的算法模型之一，它是支持向量机在函数逼近和回归估计中的应用。在SVR回归分析中，使用支持向量机可以使回归函数尽量平滑，其泛化能力强。
本文论述了支持向量回归的基本原理和思想，介绍了支持向量回归算法以及所用到 的几种常见的核函数（即线性内核、多项式内核、径向基函数内核、高斯内核）。本设计主要实现的功能有：数据集的创建、内核函数的选取、参数的设置、训练集的回归、数据集的保存与打开。通过不同核函数的选取以及相应参数的设置对输入数据集进行回归。此模型主要解决非线性回归模型的预测。通过实验改变各个参数的不同取值对训练集进行回归，并分别统计出支持向量的个数，回归性能，程序运行时间。最后对回归的结果进行分析，得出各参数对回归性能的影响。 关键词：支持向量回归; 训练算法; 核函数; 线性判别
ABSTRACT
Support vector machine (SVM) is a new method of study based on statistical learning theory which has attracted extensive attentions by academic circles both at home and abroad in recent years. It has been widely used in pattern recognition and function estimation. The biggest characteristic of support vector machine (SVM) theory is that a small error limited by the training set of sample can ensure the independent test set’s small error. Thus a support vector regression (SVR) forecasting model can be built by support vector machine (SVM) theory and it can solve various practical problems.
SVR algorithm model is one of pattern recognition algorithm, which is more widely used in approximation of function and the application of the regression estimate. In the SVR regression analysis, using support vector machine (SVM) can smooth regression function as far as possible. Its generalization ability is strong.
This paper discusses the basic principle of support vector regression and introduces support vector regression algorithm and several common kernel functions (the linear kernel, polynomial kernel and radial basis function (RBF) kernel, the Gaussian kernel etc.). This essay successfully makes these functions work: the creation of data sets, the selection of kernel function, parameter settings, return of the training set, the preservation and open of the data set. We accomplish the return of input of data set through the selection of different kernel functions and the setting of corresponding parameter. This model is mainly to solve the nonlinear regression model prediction. Then, the same issue is done through the experiment to change the values of different parameters, and the statistics, the number of support vector regression， performance of program running time are accounted. Finally, we have analysis the results of regression and gained the influence of various parameters on the return performance.
Key words: Support Vector Regression; Training Algorithms; Kernel Function; Linear Discrimination Analysis
目 录
第1章 绪论 ............................................................... 1 1.1 课题研究背景 ........................................................ 1 1.2 国内外研究现状 ...................................................... 1 1.3 课题研究目的 ........................................................ 2 1.4 课题研究使用的开发工具 .............................................. 3 1.5论文组织结构 ........................................................ 3 第2章 支持向量机回归原理 ................................................. 5 2.1 支持向量机 .......................................................... 5 2.2 支持向量回归 ........................................................ 5 2.2.1 回归初步形式 .................................................... 5 2.2.2 线性支持向量回归 ................................................ 6 2.2.3 非线性支持向量回归 .............................................. 7 2.3支持向量回归核函数 .................................................. 7 2.4 支持向量回归算法 .................................................... 8 2.4.1 支持向量回归的算法的基础 ........................................ 8 2.4.2 ??SVR回归算法 ............................................... 10 2.4.3 关于算法的几点说明 ............................................. 11 第3章 基于Matlab实现SVR的总体设计 .................................... 13 3.1 总体设计思想 ....................................................... 13 3.2 功能模块的划分及相关流程图 ......................................... 13 3.2.1 主要功能模块的划分 ............................................. 13 3.2.2 实现程序的主要框架图 ........................................... 13 3.2.3 支持向量回归模型的流程图 ....................................... 14 第4章 基于支持向量回归模型的实现 ........................................ 16 4.1模型的功能描述 ..................................................... 16 4.2 运行结果 ........................................................... 17 4.2.1 主界面 ......................................................... 17 4.2.2 功能描述界面 ................................................... 17 4.2.3运行过程及结果 .................................................. 18 4.2.4 命令窗口的显示结果 ............................................. 24 4. 3系统的性能分析及结论 ............................................... 24 第5章 总结 .............................................................. 27
致 谢 ................................................................. 28 参考文献 .................................................................. 1