使用模糊數學規劃改善支持向量機

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彭偉誠(Wei-Cheng Peng) 查詢紙本館藏

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論文名稱

使用模糊數學規劃改善支持向量機
(The use of fuzzy mathematical programming in support vector machines)

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摘要(中)

在一般典型的分類(Classification)問題中，通常只有一些模糊且攏統的資訊，以及一些來自於分類樣本的特定子集合，所以必須利用這些現有的資訊，尋找有效的方法設計一些正確的分類器。
在現有模糊支持向量機中，許多研究求解前須事先利用測量技術以獲得模糊資料的訊息；有些的求解方法則是過於複雜，因而降低了演算法的可行性。本研究則提出一種新的且有效率的模糊支持向量機(Fuzzy Support Vector Machines：FSVMs)，該決策方案直接對原始的資源量做推廣性的容忍技術，因此克服採集額外資訊的困難。
在理論建構上，合理的使用模糊不等式來表達模糊來源的線性規劃問題，這提供了加入容忍到限制式以滿足與擴大實務性的非線性系統成為可能。為了驗證這個分類器，本研究從UCI資料庫中解決幾個真實世界中的分類問題。實驗結果顯示一個具模糊限制式之模糊支持向量機能改善原支持向量機性能且能達到較低得測試誤差率。

摘要(英)

Classification approaches usually present the poor generalizeation performance with an apparent class imbalance problem. There are many researches reported in the literature that the characteristics of data sets have strongly influenced the performance of different classifiers. Unfortunately, it is necessary to get the information of fuzzy datasets by some methods in advance. These methods are too complicated to increase the utility of this algorithm. There is a latest and more efficient Fuzzy Support Vector Machines reported in this study. In addition, it uses an extensively tolerance technique to raw data directly, so as to overcome the difficulty of collecting extra information. According to the structure of the theorem, it is reasonable to use fuzzy inequalities as the fuzzy resource programming and thus adding tolerance into the constraints to satisfy and extend the reality of nonlinear programming is possible. For validating this classifier, seven true cases from UCI database are solved and these results obviously show that fuzzy membership function can improve the performance of traditional SVMs and obtain the lower rate of classification error.

關鍵字(中)

★ 歸屬函數
★ 支持向量機
★ 模糊支持向量機

關鍵字(英)

★ Fuzzy Support Vector Machines
★ Membership Function
★ Support Vector Machines

論文目次

中文摘要
英文摘要
目錄……………………………………………………………I
附圖目錄………………………………………………………III
附表目錄………………………………………………………V
第一章緒論…………………………………………………1
1.1 研究背景………………………………………………1
1.2 研究動機與目的………………………………………2
1.3 主要貢獻………………………………………………3
1.4 論文架構………………………………………………3
第二章模糊線性規劃………………………………………5
2.1 線性規劃簡介…………………………………………5
2.2 模糊理論………………………………………………7
2.2.1 明確集合與模糊集合…………………………8
2.2.2 歸屬函數之定義……………………………10
2.2.3 模糊集合表示方式…………………………11
2.2.4 模糊集合運算之種類………………………12
2.3 模糊線性規劃…………………………………………15
第三章支持向量機………………………………………20
3.1 線性支持向量機:資料可分情形……………………20
3.2 線性支持向量機:資料不可分情形…………………27
3.3 非線性支持向量機……………………………………31
3.3.1 核函數…………………………………………32
3.3.2 支持向量機非線性模型……………………… 35
第四章模糊支持向量機……………………………………39
4.1 推導模糊支持向量機…………………………………39
4.2 學習曲線………………………………………………46
4.3 辨識率之評估…………………………………………48
第五章實驗結果與討論……………………………………50
5.1資料的架構………………………………………………50
5.2 訓練和測試階段………………………………………52
5.3 Wilcoxon signed-ranks test………………………57
第六章結論和意見…………………………………………61
參考文獻…………………………………………………………63

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指導教授

鍾鴻源(Hung-Yuan Chung)

審核日期

2010-7-6

推文