摘 要
支持向量機(jī)由于其諸多的優(yōu)良特性，近年來(lái)引起了廣泛的關(guān)注，已經(jīng)成為一個(gè)十分活躍的研究領(lǐng)域。本文較全面地研究了支持向量機(jī)的理論及應(yīng)用方法，討論了支持向量機(jī)中高斯核函數(shù)參數(shù)的選擇問(wèn)題，首次將支持向量機(jī)用于測(cè)井參數(shù)屬性估計(jì)儲(chǔ)層屬性中。
本文中，首先對(duì)支持向量機(jī)的理論基礎(chǔ)——統(tǒng)計(jì)學(xué)習(xí)理論作了一個(gè)概述，主要論述了學(xué)習(xí)過(guò)程的一致性，如何控制學(xué)習(xí)過(guò)程的推廣能力等問(wèn)題，其次，對(duì)簡(jiǎn)單的線性可分?jǐn)?shù)據(jù)，詳細(xì)介紹了線性支持向量機(jī)的工作原理，即尋找具有最大的分離超平面；核函數(shù)的實(shí)質(zhì)是通過(guò)一非線性映射把原空間上非線性可分的數(shù)據(jù)映射到另一個(gè)特征空間上的線性可分?jǐn)?shù)據(jù)，然后利用與線性支持向量機(jī)完全一樣的方法，在該空間建立一個(gè)超平面，使其在原空間對(duì)應(yīng)著一個(gè)非線性超曲面，通過(guò)引入一個(gè)核函數(shù)使所有的計(jì)算在原空間完成。同時(shí)針對(duì)本文主要討論的回歸問(wèn)題給以詳細(xì)地說(shuō)明，支持向量機(jī)的解最終歸結(jié)為一個(gè)凸二次規(guī)劃，有全局最優(yōu)解。簡(jiǎn)單介紹了支持向量機(jī)較常用的訓(xùn)練算法——序貫最小優(yōu)化算法，自己編程用MATLAB實(shí)現(xiàn)了該算法,數(shù)值試驗(yàn)結(jié)果表明支持向量機(jī)具有較強(qiáng)的學(xué)習(xí)能力。另外本文具體討論了支持向量機(jī)中高斯核函數(shù)中參數(shù) 對(duì)支持向量機(jī)學(xué)習(xí)預(yù)測(cè)性能的影響，證明了參數(shù) 趨于零和無(wú)窮大情況下支持向量機(jī)的性質(zhì)，指出高斯核函數(shù)具有描述樣本相似程度這一性質(zhì)，通過(guò)數(shù)值實(shí)驗(yàn)和理論分析給出了一種選擇高斯核函數(shù)的方法——拐點(diǎn)法。進(jìn)一步指出樣本數(shù)據(jù)標(biāo)準(zhǔn)化對(duì)學(xué)習(xí)預(yù)測(cè)的影響，給出了標(biāo)準(zhǔn)化后選擇較優(yōu)高斯核函數(shù)參數(shù)的一個(gè)大致范圍。
最后根據(jù)石油地質(zhì)勘探的實(shí)際問(wèn)題，將支持向量機(jī)運(yùn)用測(cè)井曲線預(yù)測(cè)儲(chǔ)層參數(shù)——孔隙度、參透率，同時(shí)與反向傳播神經(jīng)網(wǎng)絡(luò)函數(shù)逼近法預(yù)測(cè)進(jìn)行比較，結(jié)果表明，該方法預(yù)測(cè)精度高，方法穩(wěn)定有效。支持向量機(jī)較好的解決了小樣本測(cè)井勘探的實(shí)際問(wèn)題。
關(guān) 鍵 詞：支持向量機(jī)，回歸估計(jì)，高斯核函數(shù)，測(cè)井曲線，儲(chǔ)層參數(shù)
研究類型：應(yīng)用研究

ABSTRACT
Recently, Support Vector Machines (for short SVM) attract many researchers and become a very active field because of its many good properties. SVM is a new and promising technique for classification and regression and have shown great potential in numerous machine learning and pattern recognition problems. This paper discusses the theory of SVM thoroughly, especially how choose the parameter of the Gauss kernel SVM, at last we discusses the application of SVM in predicting reservoir parameter form well log.
In the paper, we start with an overview of Statistical learning Theory which is the theoretical foundation of SVM, including the consistency of the study process, and how to control generalization of SVM. We then describe linear Support Vector Machine for separable data, which is to construct the maximal margin separating hyperplane. We explain how to introduce a nonlinear map which maps the input vectors into a feature space. In this space construct an optimal separating hyperplane using the same method, and in fact we have constructed a nonlinear decision function in the input space. We discuss the regression problem in tail at same time. The solution to SVM is a convex quadratic programmes problem at end, and it has a global optimization solution. We will briefly review some of the most common approaches before describing in detail one particular algorithm, Sequential Minimal Optimisation and then implementation it in Matlab by ourselves. The good results of many experiments show that SVM really has great generalization ability. We then focus on Gauss kernel SVM and discuss how the parameter influences the quality of SVM in tail. We also show that Gauss kernel function can describe the likeness degree of the sample. In addition, we propose a new algorithm for finding a good parameter , we called inflexion method. What's more, we point out the influence of standardize to predict, and then give mostly scope of the excellent parameter , which in Gauss kernel function after standardized.
Finally according to actual problem that in petroleum exploration and production field. We apply SVM in predicate reservoir parameter: Porosity, Permeability, from well log. Comparing this method with BP network shows that this new method can avoid the problem of the local optimal solution of BP network, and achieved the effects with higher precision. It is as an exciting method that using SVM in petroleum exploration from a few wells.
Key words: support vector machines regression Gauss kernel
well log reservoir parameter
目 錄
1 緒論 1
1.1 研究的目的和意義 1
1.2 地球物理勘探的應(yīng)用研究歷史及現(xiàn)狀 1
1.2.1 統(tǒng)計(jì)模式識(shí)別在地質(zhì)勘探中的應(yīng)用 1
1.2.2 非線性智能技術(shù)在地質(zhì)勘探中的應(yīng)用 錯(cuò)誤！未定義書簽。
1.2.3 基于小樣本的非線性智能技術(shù)在地質(zhì)勘探中的應(yīng)用 3
1.3 本文研究?jī)?nèi)容和研究方法 4
2 統(tǒng)計(jì)學(xué)習(xí)理論 6
2.1 學(xué)習(xí)問(wèn)題的表示 6
2.1.1 基于實(shí)例學(xué)習(xí)的一般模型 6
2.1.2 三種主要的學(xué)習(xí)問(wèn)題 7
2.1.3 經(jīng)驗(yàn)風(fēng)險(xiǎn)最小化歸納原理 8
2.2 統(tǒng)計(jì)學(xué)習(xí)理論的核心內(nèi)容 9
2.2.1 學(xué)習(xí)過(guò)程的一致性 9
2.2.2 學(xué)習(xí)過(guò)程收斂速度的界 12
2.2.3 控制學(xué)習(xí)過(guò)程推廣能力 14
3 支持向量機(jī) 17
3.1 支持向量簡(jiǎn)介 17
3.1.1 最優(yōu)分類面 17
3.1.2 廣義最優(yōu)分類超平面 19
3.2 分類支持向量機(jī) 20
3.2.1 高維空間中的推廣 20
3.2.2 核函數(shù) 21
3.2.3 構(gòu)造支持向量機(jī) 22
3.3 回歸支持向量機(jī) 23
3.3.1 線性支持向量回歸機(jī) 24-..