近年來許多學者在向量定量這個領域對於如何解決編碼簿製成問題以及減少啓發式
演算法的計算時間越來越感興趣。其中有一個方法主要是基於樣式簡化的方式減少啓發式演算法的計算時間。但是樣式簡化的問題在於它可能會壓縮或移除掉不應該被壓縮或移除的樣式，因此而導致結果不好。在本篇論文中，我們提出一種樣式簡化的模糊版本，稱模糊樣式簡化，它可以正確的找出應該被壓縮或移除的樣式。為了評估我們提出的方法，在本篇實驗中，我們將四種啓發式演算法：generalized Lloyd algorithm、code displacement、genetic k-means algorithm、particle swarm optimization，進行計算時間與結果的比較。最後，實驗結果發現我們提出的方法不僅可以有效的減少計算時間而且也改善了四種啓發式演算法的結果。

Recent years have witnessed increasing interest in using metaheuristics to solve the codebook generation problem (CGP) of vector quantization as well as increasing interest in reducing the computation time of metaheuristics. One of the recently proposed methods aimed at reducing the computation time of metaheuristics is based on the notion of pattern reduction (PR). The problem with PR is in that it may compress and remove patterns that are not supposed to be compressed and removed, thus decreasing the quality of the solution. In this thesis, we proposed a fuzzy version of PR called fuzzy pattern reduction (FPR) to reduce the possibility of compressing and removing patterns that are not supposed to be compressed and removed. To evaluate the performance of the proposed algorithm, we apply it to the following four metaheuristics: generalized Lloyd algorithm, code displacement, genetic k-means algorithm, and particle swarm optimization and use them to solve the CGP. Our experimental results show that the proposed algorithm can not only significantly reduce the computation time but also improve the quality of all the metaheuristics evaluated.

Contents
論文審定書i
Acknowledgments iii
摘要iv
Abstract v
List of Figures viii
List of Tables xi
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Organization of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Related Works 3
2.1 Vector Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Genetic K-means Algorithm . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Computation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Code Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Pattern Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Chapter 3 The Proposed Algorithm 15
3.1 The Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 The Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Fuzzy Pattern Reduction enhanced Particle Swarm Optimization . . . . . . . . 17
3.3.1 Detection by Voting . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.2 Fuzzy Inference Detection for pattern reduction . . . . . . . . . . . . . 20
Chapter 4 Experimental Results 23
4.1 Environment, Datasets and Parameter Settings . . . . . . . . . . . . . . . . . . 23
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.2 Computation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter 5 Conclusion 31
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Bibliography 32
Appendix A Figure Sets of Quality Chart 34
A.1 Data Set: Lena image (512 Χ 512, 256 Χ 256, 128 Χ 128) . . . . . . . . . . . . 34
A.2 Data Set: Baboon image (512 Χ 512, 256 Χ 256, 128 Χ 128) . . . . . . . . . . 35
A.3 Data Set: Peppers image (512 Χ 512, 256 Χ 256, 128 Χ 128) . . . . . . . . . . 35
Appendix B Figure Sets of Time Chart 37
B.1 Data Set: Lena image (512 Χ 512, 256 Χ 256, 128 Χ 128) . . . . . . . . . . . . 37
B.2 Data Set: Baboon image (512 Χ 512, 256 Χ 256, 128 Χ 128) . . . . . . . . . . 38
B.3 Data Set: Peppers image (512 Χ 512, 256 Χ 256, 128 Χ 128) . . . . . . . . . . 38

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