【作者】 周晓剑；

【导师】 王士同； 朱嘉钢；

【作者基本信息】 江南大学 ， 计算机软件与理论， 2008， 硕士

【摘要】 支持向量机SVM是实现统计学习理论的通用学习方法,其优异的泛化性能使得支持向量机在模式识别、回归分析和预测、密度估计等领域都得到了实际应用。当SVM用于回归分析和预测时,通常称其为支持向量回归机SVR。在回归分析中,样本数据通常含有噪声。如何选择合适的参数使得支持向量回归机SVR更具鲁棒性,从而对样本数据噪声产生尽可能强的抑制能力,是一个有着重要的理论价值和应用价值的课题。本文的主要目的就是研究当输入样本含有两种典型的噪声——拉斯噪声和均匀噪声的情况下如何选择SVR的参数使SVR具有更强的鲁棒性。首先,本文研究了Huber-SVR的鲁棒性的问题,即着重研究了当输入样本噪声为拉斯模型和均匀模型时, Huber-SVR的参数选择问题,并在贝叶斯框架下推导出了以下结论:当Huber-SVR的鲁棒性最佳时,Huber-SVR中的参数μ与输入拉斯噪声和均匀噪声的标准差σ间均呈近似线性关系。其次,本文研究了r-SVR的鲁棒性的问题,即着重研究了当输入样本噪声为拉斯模型和均匀模型时, r-SVR的参数选择问题,并在贝叶斯框架下推导出了以下结论:当r-SVR的鲁棒性最佳时, r-SVR中的参数r与输入拉斯噪声和均匀噪声的标准差σ间均呈近似线性反比关系。这两个结论亦得到了实验的证实。最后,将Huber-SVR和r-SVR用于实际股市数据回归分析,并验证上述两个结论。更多还原

【Abstract】 Support Vector Machine SVM is a general learning approach based on statistical learning theory, which has obtained its practical applications in many areas such as pattern recognition, regression and prediction, and density evaluation due to its excellent generalized capability. When applied to regression and prediction, we often call SVM as support vector regression machine SVR. In general, sample data in regression analysis often contain noise. Therefore, how to determine the optimal parameters such that SVR becomes as robust as possible is an important subject worth of studying. The main aim of this dissertation is to study the theoretical relationships between the SVR’s parameters and Laplacian and Uniform noisy inputs respectively.Firstly, in this dissertation, the issue of Huber- SVR robustness is addressed. Focused on the parameter choice issues of Huber-SVR with Laplacian and Uniform noisy inputs respectively, and based on the Bayesian framework, we derived the first relationship: with the best robustness, the approximately linear relationship between the parameterμin Huber-SVR and the standard deviationσof Laplacian and Uniform noisy inputs is kept.Secondly, the issue of r- SVR robustness is then studied. Focused on the parameter choice issues of r-SVR with Laplacian and Uniform noisy inputs respectively, and based on the Bayesian framework, we derived the second relationship: with the best robustness, the approximately inversely linear relationship between the parameter r in norm r-SVR and the standard deviationσof Laplacian and Uniform noisy inputs is kept. Meanwhile, our experimental results confirmed the above claims.Finally, Huber- SVR and r-SVR were used to regress practical stock market data respectively, and the results confirmed the above two conclusions.更多还原