【作者】 李艳；

【导师】 杨晓伟；

【作者基本信息】 华南理工大学 ， 概率论与数理统计， 2012， 硕士

【摘要】 标准支持向量机是模式识别和机器学习领域的一种很重要的分类和非线性函数估计方法，其主要的缺点是标准支持向量机模型对噪声点或孤立点较敏感。为此，Wang等人提出了双边加权模糊支持向量机模型，但其计算复杂度很高，限制了其在实际中的应用，另外设置合理的模糊隶属度函数是该模型的又一难题。针对这两个问题，本文提出如下的解决方案：1.提出了求解双边加权模糊支持向量机模型的序贯最小优化算法。为了降低双边加权模糊支持向量机模型的计算复杂度，利用SMO算法求解双边加权模糊支持向量机模型，该算法首先将整个二次规划问题分解成一系列规模为2的子问题，然后对这些子问题进行求解，最后通过实验证实了该算法的可行性。2.提出了基于双边截断损失的鲁棒支持向量机模型。双边加权模糊支持向量机模型的鲁棒性主要取决于训练样本的模糊隶属度，但是设置合理的模糊隶属度是比较困难的，针对这一难题，本文构造了基于双边截断损失的鲁棒支持向量机模型，且给出了基于凹凸过程和光滑技术的求解算法。并从理论上分析了该模型和双边加权模糊支持向量机模型的最优解之间的关系。最后通过实验表明，与标准的支持向量机模型，双边加权模糊支持向量机模型相比，该模型不仅能够降低噪声和孤立点影响而且具有较强的鲁棒性。更多还原

【Abstract】 Support vector machine (SVM) is an important methodology for classification problemsand nonlinear function estimation problems in the fields of pattern recognition and machinelearning. One of the main drawbacks in the application of the standard SVM model is that itstraining process is sensitive to outliers or noises in the training dataset. In order to reduce theeffects of the outliers, Wang et al proposed a bilateral-weighted FSVM (BW-FSVM) model.However, high computational complexity limits the applications of BW-FSVM model inpractical classification problems. And it is a difficult task how to set reasonable fuzzyrelationship degrees of the training samples. The main researches and analyses on theseproblems can be classified as follows:1. SMO algorithm for bilateral-weighted fuzzy support vector machine classifier isproposed. The SMO algorithm was proposed to reduce the computational complexity of theBW-FSVM model, which firstly decomposes the overall quadratic program (QP) problem intothe smallest possible QP sub-problems and then solves these QP sub-problems analytically.Experiment results show that the proposed method is feasible and effective.2. A bilateral-truncated-loss based robust support vector machine (BTL-RSVM) modelfor classification problems with outliers or noises is proposed. The robustness of theBW-FSVM depends greatly on the fuzzy membership degrees of the training samples.However, it is very difficult to set reasonable fuzzy membership degrees for the trainingsamples. This paper outlines the construction of BTL-RSVM model for classificationproblems with outliers or noises and an algorithm is developed to solve the problem based onthe concave-convex procedure (CCCP).Theoretically, we discuss the relationship between theoptimal solutions of the BTL-RSVM model and the BW-FSVM model. A set of experimentsis conducted to test the robustness of the BTL-RSVM model. The results indicate thatcompared with the standard SVM model and the BW-FSVM model, BTL-RSVM modelreduces the effects of the outliers or noises and provides superior robustness.更多还原