基于半径间隔界的支持向量机方法研究

发布时间：2018-04-27 19:15

本文选题：核函数 + 半径间隔界　；参考：《华南理工大学》2012年硕士论文

【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。
[Abstract]:Support Vector Machine (SVM) has become a hot research topic in recent years because of its good generalization ability for small sample problems. However, classification and prediction using SVM intelligent algorithm is a black box modeling process. The key of its good prediction accuracy and generalization ability lies in the kernel function of SVM. Therefore, most of the researches on support vector machines focus on kernel function. The research on kernel function can be summarized as several problems, such as the transformation of kernel function, combination, parameter optimization and kernel function selection. In this paper, the selection of kernel functions in support vector machines (SVM) is studied. Firstly, on the basis of the research of domestic and foreign scholars, we select the basic kernel function to construct the kernel function library, which can be divided into global kernel function and local kernel function. Then according to the evaluation criteria of generalization ability of support vector machine model, the radius interval Radius margin determined by kernel function and data sample is selected as the criterion of selecting kernel function. It should be pointed out in particular that the radius interval used in this paper is slightly different from the traditional definition. This study mainly takes into account the possibility that future predicted samples will mutate and differ greatly from the data characteristics of the training samples. Therefore, the kernel-function selection algorithm in this paper is different from the traditional optimization method of radius interval, which is used by the previous scholars, and adopts a phased optimization strategy. The first step is still the traditional support vector machine training. After calculating the kernel parameters corresponding to the kernel function and the optimal interval M), the prediction samples are introduced. The minimum hyperspherical radius in the feature space containing training and prediction samples is calculated by combining the optimal kernel parameters. In order to test the validity of this method, the paper selects the data series of oil price, gold price, the midrate data of USD / RMB, and GDP sample to carry on the empirical analysis of large sample and small sample. The results show that in the study of the single core SVR model, the radius interval of the prediction sample is negatively correlated with the prediction accuracy of the support vector machine model which selects the corresponding kernel function. Moreover, not all simple functions similar to kernel functions can be widely used as kernel functions. In the established kernel library, radial basis function and polynomial kernel function with simple structure have the best universality. Then, the optimal method of single kernel function is extended to the combination kernel function, and the convex combination of any two kernel functions in the kernel library is taken as a new combination kernel function, and the above five samples are used to test the model. In addition, considering the completeness of kernel function library, the product combination and quotient combination of kernel function are further tested. The results show that for the convex combination of two kernel functions, the radius interval bound is generally between the original radius interval bounds of two single kernels. However, due to the increase of the complexity of kernel functions, the SVR model of combined kernel is prone to the problem of overlearning (overfitting). Compared with the linear combination of kernel functions, the product combination of kernel functions does not have much advantage, but the quotient combination of kernel functions is not feasible either in theory or in practice. Finally, a new kernel function is formed by convex combination of radial basis function (RBF) kernel function and polynomial kernel function. Combining with the improved binomial tree and Monte Carlo option pricing model, the combined kernel SVR option price prediction model is constructed. The empirical results show that this method is only suitable for a small number of option price data.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TP18;F830.9

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