导　　师： 杨建辉

学科专业： 1201

授予学位： 硕士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 支持向量机（Support Vector Machine，SVM）因其对小样本问题拥有良好的泛化能力，成为近年来国内外学者研究的热点。然而，利用SVM智能算法进行分类和预测是一个黑箱建模的过程，其具有良好的预测精度以及泛化能力的关键在于SVM的核心——核函数，因此关于支持向量机的研究就大部分集中在核函数这一领域。对核函数的研究，又可概括为核函数的改造、组合、参数优化以及核函数选择等几个问题。 本文主要研究的是支持向量机中核函数的选择问题。首先，在对国内外学者的研究的基础上，选择基本的核函数组建核函数库，可分为全局核函数和局部核函数。然后根据支持向量机模型泛化能力的评价标准，选取了由核函数与数据样本共同决定的半径间隔（Radius Margin，RM）界作为选择核函数的判定指标。需要特别指出的是，本文所采用的半径间隔界与传统的定义稍有差别，本研究主要是考虑到了未来的预测样本有发生突变，与训练样本的数据特征形成较大差异的可能性，因此，本文的核函数选择算法区别于前面学者所采用的传统的半径间隔界一起优化的方法，而采用分阶段的优化策略。第一步依然是传统的支持向量机训练，在计算出核函数对应的核参数以及最优间隔（M）之后，再引入预测样本，结合最优核参数计算出包含训练和预测样本的特征空间中的最小超球半径（R）。 为检验本文方法的有效性，分别选取了石油价格、黄金价格、美元兑人民币的的汇率中间价数据序列、CPI和GDP样本对本文的方法进行了大样本和小样本的实证分析，结果表明在对单核SVR模型的研究中，融入了预测样本的半径间隔界确实与选择其对应的核函数的支持向量机模型的预测精度呈负相关关系；且并不是所有拥有与核函数形式类似的简单函数都能够作为核函数被广泛使用，在所建立的核函数库中结构简单的径向基核函数和多项式核函数的普适性最好。然后，将单核核函数的择优方法扩展到组合核函数，将核函数库中的任意两个核函数的凸组合作为新的组合核函数，并利用上述的五个样本进行模型检验。另外，考虑到核函数库的完备性，进一步检验了核函数的乘积组合与商组合。结果发现，对于两个核函数的凸组合，其半径间隔界一般会介于两单核的原半径间隔界之间，但由于核函数复杂度的增加，组合核SVR模型容易出现了过学习（过拟合）的问题。相比较于核函数的线性组合，核函数的乘积组合并没有太大的优势；而核函数的商组合无论是在理论上，还是在实际应用中都不可行。最后，采用径向基径向基核函数和多项式核函数的凸组合形成新的核函数，再结合改进的二叉树和蒙特卡罗期权定价模型，构建期权价格的组合核SVR期权价格预测模型。实证结果表明本文的方法只适合少部分期权价格数据。 As the good generalization ability of Support Vector Machine /(SVM/) to small samplesize problem, it had been a research focus in recent years. However, the process of usingSVM for classification and prediction was a black box modeling, and its precise predictionaccuracy and good generalization ability depended on the core of the SVM, kernel function.So researches on support vector machine were concentrated on the area of kernel function,which could be summarized as the transformation, combination, parameter optimization andselection of kernel functions. The main research of this paper was the selection of kernel functions of SVM. First, onthe basis of the research of domestic and foreign scholars, kernel function library wasconstituted by some basic functions, which could be divided into the global kernel functionsand local kernel functions. Second, Radius Margin /(RM/), affected by samples and kernelfunctions, was chosen to be the determination indicator of kernel functions, based on theevaluation criteria of model generalization ability of SVM. In particular, the RM used in thispaper was slightly different from the traditional definition of it. This study took into accountthe possibility of the mutation of test samples, causing a large deffernce between test samplesand training samples with data characteristics. Thus, we adopted a staged optimizationstrategy, different from the method of previous scholars, optimizing the Radius and Margin atthe same time. The first step was the traditional training of SVM; after calculating the optimalparameters of the corresponding kernel function and the Margin, the second step wascalculating the Radius of the smallest hypersphere in the feature space that contained thetraining and test samples, combined with the optimal kernel parameters. To test the effectiveness of this paper’s method, the oil spot prices, gold prices andexchange rate time series, as a large sample problem, CPI index and GDP, as small sampleproblems, were selected for the empirical analysis. The results showed that in the thesingle-kernel SVR, the Radius Margin wth test samples was negatively correlated with theprediction accuracy of SVM with the corresponding kernel function. And not all simplefunctions with the similar form of kernel functions could be used as kernel functions. In thekernel function library, the best universal kernel functions were Radial Based Function andpolynomial function with simple function structure. Furthermore, the proposed method ofselecting kernel functions was extended to the combination of kernel functions, taking theconvex combination of any two kernel functions in the kernel function library as a new kernelfunction and using of the above-mentioned five samples for model test. In addition, taking into account the completeness of the kernel function library, the product and quotientcombinations of the kernel functions were further examined. The results showed that thevalue of the Radius Margin of the convex combination was usually between that of the twooriginal kernels. But due to the increased complexity of the kernel function, the mix-kernelSVR model was prone to over learning /(over-fitting/). Compared to a linear combination ofkernel functions, a product combination did not have more advantages. And a quotientcombination was unfeasible whether in theory or in practice. Finally, combined with theimproved binary tree and Monte Carlo option pricing model, we constructed the mix-kernelSVR option price prediction model, using the convex combination of Radial Based Functionand polynomial function as the kernel function. In the empirical results, we found that theproposed method of this paper was only suitable for a small number of option price data.

关 键 词： 核函数 半径间隔界 支持向量机 期权

分 类 号： [TP18 F830.9]

领　　域： [自动化与计算机技术] [自动化与计算机技术] [经济管理]