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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳正剛(Argon Chen) | |
| dc.contributor.author | Zixin Shen | en |
| dc.contributor.author | 沈子欣 | zh_TW |
| dc.contributor.author | f01546034 | |
| dc.date.accessioned | 2022-11-24T03:34:32Z | - |
| dc.date.available | 2021-08-17 | |
| dc.date.available | 2022-11-24T03:34:32Z | - |
| dc.date.copyright | 2021-08-17 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-08-16 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/81177 | - |
| dc.description.abstract | 複回歸模型中某個獨立變數的相對重要性(Relative importance)的定義為，這個獨立變數 (independent variables) 對相依變數 (dependent variable) 變異的相對解釋能力。當各個獨立變數之間互不相關(uncorrelated)時，標準化回歸係數(standardize regression coefficient) 即可代表各變數的相對重要性，而當各獨立變數相關性較大時，即存在多重共線性時，沒有辦法再使用標準化回歸係數來看變數間的相對重要性。針對多重共線性情形，文獻上使用Dominance index [1]和Relative weight [2]來找出各獨立變數之間的相對重要性。另一方面，上述兩種相對重要性指標所針對的是複回歸模型，即一群解釋變數與一個被解釋變數之間的關係，稱之為一對多（one-to-many）關係，現實中往往需要研究一群變數與另一群變數之間的關係，這樣的問題稱為多對多（many-to-many）關係，LeBreton [3]和Hong[4]分別利用典型相關分析 (canical correlation analysis) 建立多對多關係，將Relative weight發展到多對多層面，以考量在多對多相關關係下各個變數的相對重要性，稱為“多對多相對重要性”。 在一對多關係中，Dominance index和Relative weight對資料的前提假設為樣本夠大（樣本量大於獨立變數個數），且獨立變數之間是線性獨立（linear independent）的，這種假設忽視了兩種情況，一是資料是樣本足夠，但獨立變數之間是線性相關（linear dependent）的，另一種情況樣本數 (n) 小於甚至遠小於獨立變數之個數 (p)，即高維度資料（n≪p）。同樣的，在多對多關係的分析，LeBreton [3]和Hong [4]也忽略了兩種情形，一是資料雖有足夠大樣本資料，但是兩群變數中至少有一群變數是線性相關的，另一種是兩群變數中至少有一群變數個數小於樣本量。本文即是分別針對一對多和多對多關係中，建構適用於雖樣本夠大卻非滿秩情形及樣本量不夠大的情形下各個變數的普遍型相對重要性指標。也在解決這些問題後，首次將相對重要性方法應用到變數選擇問題的應用領域。 本文使用模擬案例闡明所建構的一對多及多對多普適型相對重要性指標，並利用基因表現及半導體電信測試資料的實際案例分析驗證其在變數選擇上的應用效力，案例結果顯示本文所建構的相對重要性指標具有很好的適用性與準確性。 | zh_TW |
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| dc.description.tableofcontents | "Acknowledgements i 中文摘要 iii Abstract v Contents vii List of Figures xi List of Tables xiii Abbreviation xv Chapter 1 Introduction 1 1.1 Multiple Linear Regression and Relative Importance.........1 1.1.1 The traditional relative importance indexes in multiple linear regression..................................2 1.1.2 The limitation of relative weight analysis...............4 1.2 Many-to-many Association and Relative Importance.........5 1.2.1 The limitation of causality analysis methods in dealing with many-to-many association..........................7 1.2.2 The advantages of regression models in dealing with many-to-many association..............................8 1.2.3 The traditional relative importance indexes in canonical correlation analysis and their limitations.....................9 1.3 Research Objectives and Contributions................10 1.4 Chapter Outlines............................11 Chapter 2 Literature Review 13 2.1 Relative Weight Analysis with Full Column Rank Design Matrix...13 2.2 Canonical Correlation Analysis....................17 Chapter 3 One-to-many Comprehensive Relative Importance Analysis Based On Multiple Linear Regression 23 3.1 General Least square orthonormal Approximation..........24 3.2 Relative Importance Analysis for Singular Xn×p with n>p.....27 3.3 Comprehensive Relative Importance Analysis Based on Multiple Linear Regression.............................29 3.4 Simulation Case Study for CRI....................33 3.4.1 Simulation case 1 with grouped variables..............33 3.4.2 Simulation case 2 with power decay correlation...........36 3.5 Applications of CRI to High Dimensional Gene Expression Datasets.38 3.5.1 Experimental datasets and procedures................39 3.5.2 Experimental results..........................41 Chapter 4 Many-to-many Comprehensive Relative Importance Analysis Based on Canonical Correlation Analysis 45 4.1 The Construction of CRI_CCA....................47 4.2 The Effect Direction and Significance of CRI_CCA.........51 4.3 The Comparison of CRI_CCA and Multivariate Relative Weight...53 4.4 Simulation Study for CRI_CCA....................55 4.4.1 The comparison of CRI_CCA and CCA based indexes with simulation case................................58 4.4.2 The comparison of CRI_CCA and PLSC2A based indexes with simulation case..............................59 4.4.3 The comparison of CRI_CCA and multivariate relative weight with simulation case............................60 4.5 Applications of CRI_CCA to Semiconductor Yield Analysis.....62 4.5.1 The demonstration of nonlinear effects...............63 4.5.2 Comparison of CRI_CCA, squared canonical weight and canonical loading.................................64 4.5.3 Comparison of CRI_CCA and SEM.................69 4.5.4 Prediction abilities of the all competing indexes...........70 Chapter 5 Conclusions 73 5.1 Technical Implications and Practical Applications...........74 5.2 Limitations and Future Studies.....................75 References 77 AppendixA—Proofs91 A.1 Proof of Theorem 1...........................91 A.2 Proof of Lemma1............................95 A.3 Proof of Lemma2............................96 A.4 Proof of Lemma3............................97 A.5 Proof of Corollary1...........................97 A.6 Proof of Proposition1..........................98 A.7 Proof of Corollary2...........................101 A.8 Proof of Proposition2.........................102 A.9 Proof of Theorem3...........................103 A.10 Proof of Proposition3.........................104 A.11 Proof of Proposition4.........................105" | |
| dc.language.iso | en | |
| dc.subject | 變數選擇 | zh_TW |
| dc.subject | 變數排序 | zh_TW |
| dc.subject | 多重共線性 | zh_TW |
| dc.subject | 基因表現型資料分析 | zh_TW |
| dc.subject | 典型相關分析 | zh_TW |
| dc.subject | 多變異分析 | zh_TW |
| dc.subject | 相對重要性 | zh_TW |
| dc.subject | 多對多分析 | zh_TW |
| dc.subject | 半導體良率分析 | zh_TW |
| dc.subject | 相對權重 | zh_TW |
| dc.subject | 非滿秩 | zh_TW |
| dc.subject | 小樣本問題 | zh_TW |
| dc.subject | 高維數據分析 | zh_TW |
| dc.subject | High dimensional data analysis | en |
| dc.subject | Collinearity | en |
| dc.subject | Variable ranking | en |
| dc.subject | Variable selection | en |
| dc.subject | Small sample size | en |
| dc.subject | Singularity | en |
| dc.subject | Relative weight | en |
| dc.subject | Relative importance | en |
| dc.subject | Canonical correlation analysis | en |
| dc.subject | Multivariate analysis | en |
| dc.subject | Many-to-many analysis | en |
| dc.subject | Semiconductor yield analysis | en |
| dc.subject | Gene expression data analysis | en |
| dc.title | 普適型相對重要性分析及其應用 | zh_TW |
| dc.title | Comprehensive Relative Importance Analysis and Its Applications | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 陳中明(Hsin-Tsai Liu),陳倩瑜(Chih-Yang Tseng),楊烽正, 藍俊宏 | |
| dc.subject.keyword | 多重共線性,變數排序,變數選擇,高維數據分析,小樣本問題,非滿秩,相對權重,相對重要性,典型相關分析,多變異分析,多對多分析,半導體良率分析,基因表現型資料分析, | zh_TW |
| dc.subject.keyword | Collinearity,Variable ranking,Variable selection,High dimensional data analysis,Small sample size,Singularity,Relative weight,Relative importance,Canonical correlation analysis,Multivariate analysis,Many-to-many analysis,Semiconductor yield analysis,Gene expression data analysis, | en |
| dc.relation.page | 105 | |
| dc.identifier.doi | 10.6342/NTU202102080 | |
| dc.rights.note | 同意授權(限校園內公開) | |
| dc.date.accepted | 2021-08-16 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工業工程學研究所 | zh_TW |
| 顯示於系所單位： | 工業工程學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-0408202114481800.pdf 授權僅限NTU校內IP使用（校園外請利用VPN校外連線服務） | 1.67 MB | Adobe PDF |
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