【作者】 张斌；

【导师】 唐朝晖；

【作者基本信息】 中南大学 ， 控制科学与工程， 2010， 硕士

【摘要】 支持向量机(SVM)作为一种基于统计学习理论的新型机器学习方法,采用结构风险最小化原则以及核函数方法,有效解决了小样本学习、局部寻优和维数灾难等问题。然而,计算代价过大、核函数方法和参数寻优标准不确定性限制了SVM的应用范围。如何解决这些问题已成为SVM学习领域的研究热点之一首先介绍机器学习的概念、统计学习理论的发展过程以及SVM的主要原理,分析基于聚类原理和结构改进支持向量的约简方法。针对SVM计算代价过大的问题,提出一种改进的约简算法即两步筛选算法(2s-PSV算法)：首先,基于样本块划分和样本密度计算初步剔除训练集的冗余样本；然后,根据相对边界样本距离提取候选训练样本。该算法适应于各种分布状态的训练样本集,不仅能有效剔除异常样本,而且能避免误删支持向量。将2s-PSV算法应用于SVM中,并引入线性组合核函数构造一种改进的约简支持向量机(IS-SVM)。该IS-SVM的核函数结合局部核函数与全局核函数的优势,具备较好的局部差值能力和泛化能力,能有效映射各类分布的训练样本；2s-PSV算法剔除映射空间的异常样本,剪裁冗余样本,提取候选训练样本。对SVM和IS-SVM采用标准数据库的多维大型数据集测试,对比分析结果表明IS-SVM具有更高的训练精度和更少的训练时间。最后,将IS-SVM应用于锌湿法冶炼净化过程镉离子浓度的软测量建模过程中,仿真结果表明模型精度满足工业过程的生产标准要求。更多还原

【Abstract】 Support vector machine (SVM) proposed by Vapnik is a novel machine learning method based on the statistic learning theory. The structure risk minimization and kernel method are proposed to solve the problems with limited samples, non-linearity, high-dimension of feature space perfectly. However, the large computing cost and uncertain kernel method and standard uncertainty of parameter optimization don’t contribute to the development of SVM. Hence, the researchers have studied it for these years.Firstly, the concept of Machine learning, the development of Statistic Learning Theory and the main principles of SVM are introduced, and the reduction method based on clustering is compared with the method based on structure of SVM. Aimed at the large computing costs of SVM,2 steps Pre-extraction Support Vectors (2s-PSV) method, an improved method, is proposed. The sample space is divided into sample blocks by the given scale, then the blocks containing abnormal samples and redundant samples are rejected while the ones having candidate samples are selected. Next, the extended boundary samples picked by relative boundary distance consititute the final candidate sample set. The 2s-PSV method is suitable for the sample set with any type of distribution, and high in reduction ratio and training precision.Secondly, using the 2s-PSV method and introducing the linear hybrid kernel function, an Improved Simplified Support Vector Machine (IS-SVM) is proposed. The training samples are mapped to a high dimension feature space by the combination kernel. Then, the samples are reduced by the 2s-PSV method. The hybrid kernel consisting of Gaussian kernel and linear kernel improves the generalization and interpolation of IS-SVM. And 2s-PSV method cuts the redundant samples and extracts the candidate samples, increases the calculation accuracy and decreases the computing time of IS-SVM. To prove the effectiveness of IS-SVM, SVM and IS-SVM are tested respectively by big multi-dimensional data sets from UCI Machine Learning Repository. The comparison shows that the IS-SVM is higher in training precision and lower in computational complexity.Finally, IS-SVM is applied to the soft-sensing model of cadmium ion concentration in purification process of zinc hydrometallurgy. The simulation results show that the precision of IS-SVM satisfies the requirement of industrial production.更多还原