【作者】 朱嘉钢；

【导师】 王士同；

【作者基本信息】 南京理工大学 ， 模式识别与智能系统， 2005， 博士

【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常见的两种SVR的参数与输入样本数据的噪声间的关系，从而为鲁棒的SVR的参数选择提供理论依据。 首先研究了SVR的鲁棒性的问题，即着重研究了当输入样本噪声为高斯模型时，Huber-SVR和r范数-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SVR的鲁棒性最佳时，Huber-SVR中的参数μ与输入高斯噪声的标准差σ间呈近似线性关系；r范数-SVR的参数r与输入高斯噪声的标准差σ间呈近似线性反比关系。这两个结论亦得到了实验的证实。 还以图像恢复为应用背景，研究应用SVR对图像脉冲噪声的识别问题。在最新的应用SVM识别脉冲噪声的研究成果的基础上，研究了如何提高脉冲噪声识别正确率的问题，提出了基于SVR的脉冲噪声滤波器和利用小波变换的改进的SVM脉冲噪声滤波器，实验表明这两种滤波器在不同的应用背景下可以明显地改善滤波效果。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 the noisy inputs.Firstly, the issue of SVR robustness is addressed. Focused on the parameter choice issues of Huber-SVR and norm r-SVR with Gaussian noisy inputs respectively, and based on the Bayesian framework, we derived the two following relationships: (1) with the best robustness, the approximately linear relationship between the parameter μ in Huber-SVR and the standard deviation a of Gaussian noisy input is kept, (2) the approximately inversely linear relationship between the parameter r in norm r-SVR and the standard deviation σ of Gaussian noisy input is kept. Our experimental results confirmed the above claims.Accordingly, on how to recognize pulse noise in image using SVR is investigated. Based on the latest research results on recognizing pulse noise in image using SVM, the two new pulse noise image filters are proposed. One uses SVR to recognize pulse noise, the other combines wavelet transforms with SVC to recognize pulse noise. Experimental results demonstrated the effectiveness of these two new image filters.更多还原