本文選題：核函數(shù) + 半徑間隔界�。� 參考：《華南理工大學(xué)》2012年碩士論文

【摘要】：支持向量機(jī)（Support Vector Machine，SVM）因其對(duì)小樣本問題擁有良好的泛化能力，成為近年來國內(nèi)外學(xué)者研究的熱點(diǎn)。然而，利用SVM智能算法進(jìn)行分類和預(yù)測(cè)是一個(gè)黑箱建模的過程，其具有良好的預(yù)測(cè)精度以及泛化能力的關(guān)鍵在于SVM的核心——核函數(shù)，因此關(guān)于支持向量機(jī)的研究就大部分集中在核函數(shù)這一領(lǐng)域。對(duì)核函數(shù)的研究，又可概括為核函數(shù)的改造、組合、參數(shù)優(yōu)化以及核函數(shù)選擇等幾個(gè)問題。 本文主要研究的是支持向量機(jī)中核函數(shù)的選擇問題。首先，在對(duì)國內(nèi)外學(xué)者的研究的基礎(chǔ)上，選擇基本的核函數(shù)組建核函數(shù)庫，可分為全局核函數(shù)和局部核函數(shù)。然后根據(jù)支持向量機(jī)模型泛化能力的評(píng)價(jià)標(biāo)準(zhǔn)，選取了由核函數(shù)與數(shù)據(jù)樣本共同決定的半徑間隔（Radius Margin，RM）界作為選擇核函數(shù)的判定指標(biāo)。需要特別指出的是，本文所采用的半徑間隔界與傳統(tǒng)的定義稍有差別，本研究主要是考慮到了未來的預(yù)測(cè)樣本有發(fā)生突變，與訓(xùn)練樣本的數(shù)據(jù)特征形成較大差異的可能性，因此，本文的核函數(shù)選擇算法區(qū)別于前面學(xué)者所采用的傳統(tǒng)的半徑間隔界一起優(yōu)化的方法，而采用分階段的優(yōu)化策略。第一步依然是傳統(tǒng)的支持向量機(jī)訓(xùn)練，在計(jì)算出核函數(shù)對(duì)應(yīng)的核參數(shù)以及最優(yōu)間隔（M）之后，再引入預(yù)測(cè)樣本，結(jié)合最優(yōu)核參數(shù)計(jì)算出包含訓(xùn)練和預(yù)測(cè)樣本的特征空間中的最小超球半徑（R）。 為檢驗(yàn)本文方法的有效性，分別選取了石油價(jià)格、黃金價(jià)格、美元兌人民幣的的匯率中間價(jià)數(shù)據(jù)序列、CPI和GDP樣本對(duì)本文的方法進(jìn)行了大樣本和小樣本的實(shí)證分析，結(jié)果表明在對(duì)單核SVR模型的研究中，融入了預(yù)測(cè)樣本的半徑間隔界確實(shí)與選擇其對(duì)應(yīng)的核函數(shù)的支持向量機(jī)模型的預(yù)測(cè)精度呈負(fù)相關(guān)關(guān)系；且并不是所有擁有與核函數(shù)形式類似的簡(jiǎn)單函數(shù)都能夠作為核函數(shù)被廣泛使用，在所建立的核函數(shù)庫中結(jié)構(gòu)簡(jiǎn)單的徑向基核函數(shù)和多項(xiàng)式核函數(shù)的普適性最好。然后，將單核核函數(shù)的擇優(yōu)方法擴(kuò)展到組合核函數(shù)，將核函數(shù)庫中的任意兩個(gè)核函數(shù)的凸組合作為新的組合核函數(shù)，并利用上述的五個(gè)樣本進(jìn)行模型檢驗(yàn)。另外，考慮到核函數(shù)庫的完備性，進(jìn)一步檢驗(yàn)了核函數(shù)的乘積組合與商組合。結(jié)果發(fā)現(xiàn)，對(duì)于兩個(gè)核函數(shù)的凸組合，其半徑間隔界一般會(huì)介于兩單核的原半徑間隔界之間，但由于核函數(shù)復(fù)雜度的增加，組合核SVR模型容易出現(xiàn)了過學(xué)習(xí)（過擬合）的問題。相比較于核函數(shù)的線性組合，核函數(shù)的乘積組合并沒有太大的優(yōu)勢(shì)；而核函數(shù)的商組合無論是在理論上，，還是在實(shí)際應(yīng)用中都不可行。最后，采用徑向基徑向基核函數(shù)和多項(xiàng)式核函數(shù)的凸組合形成新的核函數(shù)，再結(jié)合改進(jìn)的二叉樹和蒙特卡羅期權(quán)定價(jià)模型，構(gòu)建期權(quán)價(jià)格的組合核SVR期權(quán)價(jià)格預(yù)測(cè)模型。實(shí)證結(jié)果表明本文的方法只適合少部分期權(quán)價(jià)格數(shù)據(jù)。
[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.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TP18;F830.9

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