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System No. U0002-2007201012424700
Title (in Chinese) 模糊支援向量迴歸之構建與分析
Title (in English) Analysis for fuzzy support vector regression model
Other Title
Institution 淡江大學
Department (in Chinese) 管理科學研究所碩士班
Department (in English) Graduate Institute of Management Science
Other Division
Other Division Name
Other Department/Institution
Academic Year 98
Semester 2
PublicationYear 99
Author's name (in Chinese) 梁耀云
Author's name(in English) Yao-Yun Liang
Student ID 697621067
Degree 碩士
Language Traditional Chinese
Other Language
Date of Oral Defense 2010-06-23
Pagination 75page
Committee Member advisor - Ruey-Chyn Tsaur
co-chair - 傅敬群
co-chair - 陳怡妃
Keyword (inChinese) 支援向量機
模糊迴歸
支援向量迴歸
Keyword (in English) Supper Vector Machine
Fuzzy Regression
Supper Vector Regression Machine
Other Keywords
Subject
Abstract (in Chinese)
近年來,學者們利用支援向量機的基本想法於多變量模糊(非)線性迴歸,獲得求解的計算效率。然而求解模糊支援向量迴歸模式仍然複雜,並且當參數皆為模糊數(例如: )時仍無法求解,因此我們採用Carlsson & Fuller (2001) 提出的模糊數可能性平均數當作限制式,建構了更簡易求解的模糊支援向量迴歸模式,依照參數定義為模糊數與否一共有了六種不同的模式。
    透過在資料分析的圖中,我們可以發現模式5  求解出的預測結果與原始資料配置的程度相當高,以誤差均方根(Root Mean Square Error ; RMSE)越小,模型預測精確度越高的特性來衡量預測模型優劣,RMSE達到了1.3134。於是我們根據 Carlsson & Fuller (2001) 提出的模糊數可能性平均數這個概念,所建構的模糊支援向量迴歸模式是一個可行的方法,並且應用於預測上相當精準。
Abstract (in English)
In recent years,introduce the use of SVM for multivariate fuzzy linear and nonlinear regression models with efficiency solutions. However, fuzzy support vector regression model is still complicated to slove the parameters which are all fuzzy numbers. In order to cope with this problem, we adopt the fuzzy possibilistic mean method proposed by Carlsson & Fuller (2001)which is more easily to slove fuzzy support vector regression model. According to parameters are fuzzy numbers or not, there are six kinds of models.
Fnally, in data analysis, we can find forecasting vales in our proposed models are fitting very well using RMSE. It is obviously that our proposed fuzzy support vector regression model can be applied to forecast with better forecasting performance
Other Abstract
Table of Content (with Page Number)
目錄
目錄	I
圖目錄	III
表目錄	IV
第一章 緒論	1
1.1 研究背景與動機	1
1.2 研究目的	2
1.3 論文架構	2
第二章 文獻探討	4
2.1 模糊理論簡介	4
2.2 模糊集合與 level集合	5
2.3 模糊數及其運算	6
2.4 模糊迴歸模式簡介 	9
2.5 模糊迴歸模式發展近況	9
2.5.1 模糊迴歸模式之構建	10
2.5.2 模糊迴歸模式之參數估計	11
2.6 支援向量機簡介	14
2.7 支援向量迴歸	14
2.7.1 線性支援向量迴歸估計	15
2.7.2 非線性支援向量迴歸估計	20
2.8 模糊支援向量迴歸	24
2.9 模糊數之可能性期望值	26
第三章 模糊支援向量迴歸模式	28
3.1 模糊支援向量迴歸對偶模式	43
第四章 資料分析	56
4.1 模糊支援向量迴歸模式之確立:以模式1為例	58
4.2 其他模式之資料分析結果	64
第五章 結論與未來研究	71
5.1 結論	71
5.2 未來研究	72
參考文獻	73
 
圖目錄
圖1.1 研究流程圖	3
圖2.1    -LEVEL集合	6
圖2.2大約5的模糊數	6
圖2.3 梯型模糊數的歸屬函數圖形	7
圖2.4 三角型模糊數的歸屬函數圖形	8
圖2.5  、 與 的關係與位置分佈	10
圖 2.6  、 和 的關係對應圖	12
圖2.7  線性支援向量迴歸模式示意圖	15
圖2.8資料為非線性分類	20
圖2.9 資料映射到特徵空	20
圖2.10 資料由輸入空間轉換至特徵空間	21
圖4.2 模式1限制式為上界及中心值之概念與原始資料分析比較	60
圖4.3 模式1限制式為上界及中心值之概念與原始資料分析比較	62
圖4.4 模式1限制式為上界及下界之概念與原始資料分析比較	63
圖4.5 模式2之模糊支援向量迴歸模式與原始資料分析比較	65
圖4.6 模式 5之模糊支援向量迴歸模式與原始資料分析比較	66
圖4.7 模式6 之模糊支援向量迴歸與原始資料分析比較	67
圖4.8模式3之模糊支援向量迴歸模式與原始資料分析比較	69
圖4.9 模式 4之模糊支援向量迴歸與原始資料分析比較	70


 
表目錄
表4.1 模糊輸入資料與模糊輸出資料	57
表4.2 明確輸入資料與模糊輸出資料	57
表4.3 試行數值之RMSE	58
表4.4 求解限制式為上界、中心值及下界之概念結果	59
表4.5 試行數值之RMSE	60
表4.6求解限制式為上界及中心值之概念結果	60
表4.7 試行數值之RMSE	61
表4.8求解限制式為下界及中心值之概念結果	61
表4.9 試行數值之RMSE	62
表4.10求解限制式為上界及下界之概念結果	63
表4.11 試行數值之RMSE	64
表4.12求解模式2之模糊支援向量迴歸結果	64
表4.13 試行數值之RMSE	65
表4.14求解模式 5之模糊支援向量迴歸模式結果	66
表4.15 試行數值之RMSE	67
表4.16求解模式6之模糊支援向量迴歸模式結果	67
表4.17 試行數值之RMSE	68
表4.18求解模式3之模糊支援向量迴歸模式結果	68
表4.19 試行數值之RMSE	69
表4.20求解模式 4之模糊支援向量迴歸模式結果	70
References
一、英文參考文獻
1.   B.E. Boser, I.M. Guyon, and V. Vapnik. 1992. A training algorithm for optimal margin classifiers. Proceedings of the Fifth annual workshop on Computational learning theory. Pittsburgh, Pennsylvania, United States : 144-152. 
2.   A. Bellili, M. Gilloux and P. Gallinari. 2001. An hybrid mlp-svm handwritten digit recognizer. International Conference on Document Analysis and Recognition.
3.   A. Celmins. 1987. Least Squares Model fitting to fuzzy vectoe data. Fuzzy Sets and Systems. 22: 669-690
4.   C. Carlsson and R. Fuller. 2001. On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and System. 122: 315-326.
5.   C. Cortes and V. N. Vapnik. 1995. Support vector networks. Machine Learning. 20: 273-297.
6.   P. Diamond. 1988. Fuzzy least square. Information Sciences. 46: 141-157.
7.   S. Gunn. 1998. Support vector machines for classification and regression. ISIS Tech. 
     Report. University of Southampton.
8.   G. Guo, S. Z. Li and K. L. Chan. 2001. Support Vector Machines for Face Recognition. Image And Vision Computing. 19 : 631-638.
9.   D. H. Hong and C. Hwang. 2003. Support vector fuzzy regression machines.  
     Fuzzy Sets and Systems. 138: 271–281. 
10.  P. Y. Hao and J. H. Chiang. 2003. A fuzzy model of support vector regression   machine. IEEE Int. Conf. On Fuzzy Systems. 1: 738-742.
11.  P. Y. Hao and J. H. Chiang. 2007. A fuzzy model of support vector regression   machine. International Journal of Fuzzy Systems. 9(1): 45-50.
12.  T. Joachimes. (1996). Text categorization with support vector machines. Technical Report . ftp://ftp-ai.informatik.unidortmund.de/pub/Reports/report23.ps.z.
13.  K.J. Kim, H. Moskowitz and M. Koksalan. 1996. Fuzzy versus statistical linear 
regression. European Journal of Operation Research. 92: 417-434.
14.  M. Sakawa and H. Yano. 1992. Multiobjective fuzzy linear regression analysis for 
fuzzy input-output data. Fuzzy Sets and Systems. 47: 173-181.
16.  M. Schmidt. (1996). Identifying speaker with support vector networks. Interface ‘96 Proceedings, Sydney.
17   K. Shima, M. Todoriki and A. Suzuki. 2004. SVM-Based Feature Selection of Latent Semantic Features. Pattern Recognition. 25 : 1051-1057.
18.  Simek, K. Fujarewicz, A. Swierniak, M.Kimmel and B. Jarzab. 2004. Using SVD and SVM Methods for Selection, Classification, Clustering and Modeling of DNA Microarray Data. Engineering Applications of Artificial Intelligence. 17 : 417-427.
19.  Takeuchi and N. Collier. 2005. Bio-Medical Entity Extraction Using Support Vector Machines. Artificial Intelligence in Medicine. 33 : 125-137.
20.  Tanaka, S. Uejima, and K. Asai. 1982. Linear regression analysis with fuzzy model.                          
     IEEE Trans. System, Man and Cybernet.12 (6) : 903-907.
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     Systems. 24 : 363-375.
22.  V.N. Vapnik. 1995. The Natural of Statistical Learning Theory. second edition. New
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23.  V. Vapnik , S. Golowich, and A. Smola. (1997). Support vector method for function
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information Processing System. 9 : (281–287). Cambridge: MIT Press.
24.  V.N. Vapnik. 1998. Statistical Learning Theory. New York :Wiley.
二、中文參考文獻
25.  王文俊。2005。認識Fuzzy。三版,1-1-6-2。台北:全華科技圖書公司。
26.  吳柏林。2005。模糊統計導論:方法與應用。初版,135-144。台北:五南出版社。
27.  陳耀茂。1999。模糊理論 = Fuzzy theory。初版,1-77。台北:五南出版社。
28.  劉天祥、佟中仁。1993。Fuzzy理論入門。初版,1-96。台北:中國生產力中心。
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