【作者】 刘勇；

【导师】 刘小茂；

【作者基本信息】 华中科技大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 支持向量机(SVM)是九十年代中叶Vapnik教授领导的研究小组提出的一种新的智能机器,源于七十年代迅速发展起来的统计学习理论,特别是体现了结构风险最小化的思想和方法。由于具有较完备的理论基础和较好的学习性能,能很好地解决小样本、非线性、高维数和局部极小点等实际问题,因而成为机器学习理论的研究热点。SVM在很多领域都得到了成功的应用,如模式识别、回归估计、函数逼近等。但是作为一种新兴技术,SVM在很多领域的研究还有待于探索和完善,如何设计快速有效的回归估计算法就是SVM实际应用中的问题之一。本文主要研究了支持向量机回归算法,并对它进行了改进,主要工作如下:首先概要介绍了支持向量机的基本原理,并对最小二乘回归估计和支持向量机回归估计算法进行了研究和比较。而后,在此基础上通过理论推导,提出一种改进的支持向量机回归估计算法,我们称之为SVR-LS方法。接着,用SVR-LS方法对Sinc函数进行回归逼近,并与LSE方法和SVR方法的实验结果进行了对比,我们发现新方法在拟合逼近方面也有着不错的效果。最后,我们将SVR-LS算法和标准的支持向量机回归估计算法应用于两个不同的数据集进行回归估计,从学习速度和精度两个方面对两种算法进行了实验分析比较,结果表明SVR-LS算法优于标准的支持向量机回归估计算法。更多还原

【Abstract】 Support vector machines (SVM) is a new kind of intelligent machine presented by Vapnik and his study group in the middle of the 1990Th. SVM is based on statistical learning theory developed in the 1970Th. It embodies the theory of structure risk minimization (SRM). Because it has quite perfect theoretical properties and good learning performance, and can solve some practical problems with low sample size, non-linearity, high-dimension of feature space and local minimization, SVM becomes a hot spot of machine learning theory.SVM has successful applications in many fields, such as pattern recognition, regression estimation, function approaching and so on. However, as a new technique, SVM still has many problems that need to be studied and improved, and researches in regression estimation based on SVM need to be enhanced. How to design fast and efficient SVM algorithms applied to regression estimation becomes a great challenge in practical applications of support vector machines.In this paper, we have learned some regress algorithms and proposed several developed Support Vector Regression (SVR). The main works are as follows:First of all, the principles of SVM are reviewed and the relationship between Least Square Estimation (LSE) and regression estimation algorithms of SVM (SVR) are compared and analyzed. Secondly, an improved regression estimation algorithm named SVR-LS is presented by theoretical deduction. And then, the proposed SVR-LS algorithm is applied to approaching the function of Sinc. Comparing to experimental results of the SVR and LES algorithm, we find that the new algorithm has good effect in function approaching. Finally, the proposed SVR-LS algorithm and normal regression estimation algorithm of SVM are applied to regression estimation of two different data sets, and learning speed and learning precision in regression are compared between the two algorithms. The experimental results show that the proposed SVR-LS algorithm is better than the normal regression estimation algorithm of SVM.更多还原