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研究生：	李思源 Lee, Szu-Yuan
論文名稱：	資料驅動空間填充抽樣在監督式與非監督式學習 Data Driven Space Filling Sampling in Supervised and Semi Supervised Learning
指導教授：	陳瑞彬 Chen, Ray-Bing
學位類別：	碩士 Master
系所名稱：	管理學院 - 統計學系 Department of Statistics
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	28
中文關鍵詞：	資料驅動空間填充抽樣、差異性、代表性樣本、初始標記
外文關鍵詞：	Data driven space-filling sampling, Discrepancy, Representative sample, Initial labeling
相關次數：	點閱：68 下載：1
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為了在大多數學習任務中取得更好的效果，我們會希望我們的訓練樣本對於母體來說是最具有代表性的。為了實現這一目標，我們認為訓練樣本應滿足空間填充的性質。但是，傳統的空間填充設計不能直接使用，因為我們只有一組採樣點，而沒有連續的實驗空間。因此，這裡採用 [15] 中提出的資料驅動的空間填充抽樣，希望可以在分類問題下搭配包含監督式與半監督式學習的方法，進而從中看到其方法之效果。除了模擬研究以外，本文還說明了一些實際資料的應用。

To achieve better performance in most of the learning tasks, we want that the training samples are the most representative to the population. To achieve this goal, we think that the training samples should satisfy the space-filling property. However, the traditional space-filling design cannot be used directly, because we only have a set of sample points, not a continuous experimental space. Thus the data driven space-filling sampling proposed in [15] is adopted here and we want to see its effects in (semi-) supervised learning approaches for the classification problems. In addition to the simulation studies, several real data are also illustrated in this thesis.

摘要 ........................................................................................ i
Abstract ................................................................................. ii 
Acknowledgements ................................................................ iii 
Table of Contents ................................................................... iv 
List of Tables .......................................................................... v 
List of Figures ......................................................................... vi
Chapter 1. Introduction ............................................................ 1
Chapter 2. Data Driven Space-Filling Sampling ....................... 2
2.1. Discrepancy ...................................................................... 2
2.1.1. Star Discrepancy ............................................................. 3 
2.1.2. F-Discrepancy ................................................................ 3
2.2. Uniform Design and Space-Filling Design ......................... 4 
2.3. DataDrivenSpace-FillingSampling ..................................... 5 
2.4. Illustrations ....................................................................... 6
2.4.1. Case1: single core, spread widely ................................... 6 
2.4.2. Case2: two cores ............................................................ 8 
2.4.3. Case3: four cores, spread widely ................................... 10 
2.4.4. Case4: four cores, extreme high-density ....................... 12
Chapter 3. Simulation Study .................................................... 15
3.1. Experimental Settings ........................................................ 15 
3.2. Simulated Data .................................................................. 15
Chapter 4. Experimental Results ............................................... 18
4.1. The Effect of the Number of Principal Components ........... 18 
4.2. Supervised Learning .......................................................... 20 
4.3. Semi-Supervised Learning ................................................. 22
Chapter 5. Conclusion and Future Work .................................... 26
References ................................................................................ 27
                                    

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校內：2025-07-19公開
校外：2025-07-19公開

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