本校學位論文庫
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論文詳情
晏宇欣
葛東嬌
數據科學學院
數據科學碩士學位課程(中文學制)
碩士
2023
多變數函數對函數回歸的函數型Takagi-Sugeno模糊系統
Takagi-Sugeno Functional Fuzzy System for Multivariate Function-on-Function Regression
數據科學 ; 模糊系統 ; 函數對函數回歸 ; 函數型主成分分析 ; 函數型聚類
Fuzzy systems ; function-on-function regression ; functional principal component analysis ; functional clustering
公開日期：28/6/2027
使用模糊邏輯進行多變量函數對函數回歸，是對模糊系統及函數型數據分析（FDA）兩個領域的一項重要進展。本文提出了Takagi-Sugeno多變量函數模糊系統（T-S mFFS），這種新方法利用模糊系統的可解釋性和靈活性，解決了函數數據中的複雜關係。模型接受多個函數數據輸入并輸出單一結果（MISO），並通過一系列的“IF-Then”規則來構建輸出的線性模型，這些模型具有雙變量斜率函數。為了識別這一系統，采用了專門的方法，利用函数型主成分分析（FPCA）進行曲線擬合，多變量函數數據聚類來確定規則數量，以及最小化二次損失函數來識別斜率函數。本文通過使用來自多個領域的真實數據集進行的比較分析，驗證了所提出系統的有效性。本研究認為該算法有潛力應用於醫療數據，並有待進一步分析。本研究著重於將模糊邏輯與函數回歸相結合，開發穩健且可解釋的高維數據模型的重要性。
The use of Takagi-Sugeno fuzzy logic in Functional Data Analysis (FDA) for multivariate function-on-function regression represents a significant advancement in both fields. This thesis introduces the Takagi-Sugeno Multivariate Functional Fuzzy System (T-S mFFS), a novel approach that leverages the interpretability and flexibility of fuzzy systems to address the complex relationships in functional data. This innovative model accepts multiple functional data inputs and produces single outputs(MISO), constructed using a series of "IF-Then" rules that output a linear model of the multivariate data with bivariate slope functions. To identify this system, a specialized approach is implemented, utilizing functional principal component analysis (FPCA) for curve fitting, multivariate functional data clustering to determine the rule number, and minimization of a quadratic loss function to identify slope functions. The proposed system demonstrates its efficacy through comparative analysis with state-of-the-art models, utilizing real datasets from various domains. The application to FDA presents a novel perspective, with potential implications for biomedical data analysis pending empirical validation. This research underscores the importance of combining fuzzy logic with functional regression to develop robust and interpretable models for high-dimensional functional data.
2024
英文
231
Acknowledgments I
摘 要 II
Abstract III
Table of Contents IV
Table of Figures VI
Table of Tables XXI
Chapter 1 Introduction 1
1.1 Context and Significance 1
1.2 Research Questions 3
1.3 Research Objectives 5
Chapter 2 Background and Related Work 7
2.1 Multivariate Function-on-Function Regression 7
2.1.1 Functional Data Basics 8
2.1.2 Function-on-Function Regression 26
2.1.3 Multivariate Functional Regression 27
2.2 Takagi-Sugeno Fuzzy System-Based Regression 33
2.2.1 Fuzzy Systems 33
2.2.2 Takagi-Sugeno Fuzzy System 40
2.2.3 Fuzzy Systems in Function-on-Function 41
Chapter 3 Takagi-Sugeno Multivariate Functional Fuzzy System 44
3.1 T-S Multivariate Functional Fuzzy System the Model and its Identification Problem 45
3.2 Identification Approach for T-S mFFS 48
3.2.1 Data preprocessing 48
3.2.2 Identifying the rule number and antecedent parameters 49
3.2.3 Identifying the consequent parameters 50
Chapter 4 Numerical Examples 55
4.1 Ocean 57
4.2 Air Quality 64
4.3 Bike sharing 71
4.4 Population Growth 78
4.5 Sanitation Mortality 87
4.6 Agriculture 99
Chapter 5 Extra Benchmark Examples: Airports 108
5.1 airports-24 108
5.1.1 Changchun 108
5.1.2 Guilin 119
5.1.3 Hefei 130
5.1.4 Huhehaote 141
5.1.5 Kunming 152
5.1.6 Nanjing 163
5.1.7 Sanya 174
5.2 airports-48 185
5.2.1 Beijing 185
5.2.2 Guangzhou 196
5.2.3 Taipa 207
Chapter 6 Conclusion and Future Work 218
6.1 Conclusion 218
6.2 Future Work 219
6.3 Expanding Applications in Various Domains 221
Reference 223
摘 要 II
Abstract III
Table of Contents IV
Table of Figures VI
Table of Tables XXI
Chapter 1 Introduction 1
1.1 Context and Significance 1
1.2 Research Questions 3
1.3 Research Objectives 5
Chapter 2 Background and Related Work 7
2.1 Multivariate Function-on-Function Regression 7
2.1.1 Functional Data Basics 8
2.1.2 Function-on-Function Regression 26
2.1.3 Multivariate Functional Regression 27
2.2 Takagi-Sugeno Fuzzy System-Based Regression 33
2.2.1 Fuzzy Systems 33
2.2.2 Takagi-Sugeno Fuzzy System 40
2.2.3 Fuzzy Systems in Function-on-Function 41
Chapter 3 Takagi-Sugeno Multivariate Functional Fuzzy System 44
3.1 T-S Multivariate Functional Fuzzy System the Model and its Identification Problem 45
3.2 Identification Approach for T-S mFFS 48
3.2.1 Data preprocessing 48
3.2.2 Identifying the rule number and antecedent parameters 49
3.2.3 Identifying the consequent parameters 50
Chapter 4 Numerical Examples 55
4.1 Ocean 57
4.2 Air Quality 64
4.3 Bike sharing 71
4.4 Population Growth 78
4.5 Sanitation Mortality 87
4.6 Agriculture 99
Chapter 5 Extra Benchmark Examples: Airports 108
5.1 airports-24 108
5.1.1 Changchun 108
5.1.2 Guilin 119
5.1.3 Hefei 130
5.1.4 Huhehaote 141
5.1.5 Kunming 152
5.1.6 Nanjing 163
5.1.7 Sanya 174
5.2 airports-48 185
5.2.1 Beijing 185
5.2.2 Guangzhou 196
5.2.3 Taipa 207
Chapter 6 Conclusion and Future Work 218
6.1 Conclusion 218
6.2 Future Work 219
6.3 Expanding Applications in Various Domains 221
Reference 223
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