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Research on Support Vector Machine Based on Radius Margin Bound

Author: LiLong
Tutor: YangJianHui
School: South China University of Technology
Course: Management decision-making and system theory
Keywords: Kernel Function Radius Margin Support Vector Machine Option
CLC: TP18
Type: Master's thesis
Year: 2012
Downloads: 46
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Abstract


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.

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