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系統識別號 U0002-2505200615111100
中文論文名稱 粒子群演算法為基礎的演化式學習-系統設計及其應用
英文論文名稱 PSO-Based Evolutionary Learning : System Design and Applications
校院名稱 淡江大學
系所名稱(中) 電機工程學系博士班
系所名稱(英) Department of Electrical Engineering
學年度 94
學期 2
出版年 95
研究生中文姓名 陳慶逸
研究生英文姓名 Ching-Yi Chen
學號 891350018
學位類別 博士
語文別 英文
口試日期 2006-05-19
論文頁數 169頁
口試委員 指導教授-余繁
委員-蘇木春
委員-許獻聰
委員-詹益光
委員-翁慶昌
中文關鍵字 粒子群演算法  群聚分析  群聚驗證  向量量化  類神經網路 
英文關鍵字 Particle Swarm Optimization  Cluster analysis  Cluster Validity  Vector Quantization  Fuzzy c-means  Neural Networks 
學科別分類
中文摘要 本論文回顧了演化式計算的重要方法和技術,從而探討粒子群演算法(PSO)及其在資料探勘、影像壓縮和類神經網路的應用。針對不同的處理問題,我們分析並結合不同的輔助機制來設計粒子群演算法的學習架構,以期得到有效的PSO系統應用平台(framework)。粒子群演算法是主要的演化式計算技術之一,它應用生物群體透過簡單模仿和跟隨其他個體而產生(emergent)系統自我組織和演化的概念,發展出最佳化演算法。PSO利用模仿群體性生物的社會行為(social-only model)取向和個體認知(cognition-only model)取向的機率性選擇來搜尋高維度問題空間的最佳解,其演算法相當簡單快速,解題原理又可以有效避開區域最小值,對於多模態最佳解(multi-modal)問題提供了一個相當良好的解決方案。在論文的第一部分,我們引進兩種以PSO為基礎的群聚分析演算法。首先我們提出一個結合指數型態距離與K-means運算法則的分割式群聚分析架構,它經由使用者在預設群聚數目的條件下產生最佳的分群結果。第二種PSO群聚分析演算法則是整合群聚驗證方法來得到資料探勘問題的最佳群聚數目以及群聚中心,以達到自動分群的目的。論文的第二部分在於提出一個應用在影像壓縮的模糊PSO向量量化器,該方法透過PSO參數學習和模糊推論生成影像向量的最佳化碼簿。相較於傳統的LBG方法,我們所提的架構更具有效性以及強健性。論文的最後一個部分致力於PSO在放射狀基底函數(RBF)神經網路的應用。針對網路的隱藏層節點與權重等參數,我們先使用正規化型式的Fuzzy c-means演算法(NFCM)進行粗略式(coarse-level)的結構鑑別,再經由結合遞迴式最小平方法則的PSO演算法作細部調整(fine tuning-level)的訓練;此一創新方法除了能以極小數量的PSO族群來達到實現RBF神經網路訓練的目的之外,其建模的性能和效率表現也得到很大的提升。本論文主要貢獻在於提出粒子群演算法的系統化的學習架構及其在工程設計最佳化問題領域的應用;基於此一泛用架構,未來我們得以快速發展出各種可靠的、高效能的工程最佳化系統。
英文摘要 The new paradigm of Swarm Intelligence, called Particle Swarm Optimization (PSO), is one of the well-known evolutionary computation techniques, which can be considered as an efficient tool to find near optimal solution in a searching space. Especially, PSO is a useful method when the problems to be solved are high-dimensional, nonlinear or some specific information is unavailable. PSO combines the social-only model and the cognition-only model to select the adjustable parameters to approach optimal solution, its main advantage is its rapid convergence and small computational requirements, which make it a good candidate for solving optimization problems. In this dissertation, the efficient, robust, and flexible PSO algorithms are proposed to generate some artificial intelligence system in solving some applications, such as cluster analysis, image processing, and neural network training.
The first task of this dissertation introduces two types of PSO clustering applications. The first one is given in advance the optimal number of clusters by manual manipulation, and then the PSO is applied to achieve the optimal clustering results. The other one is to use PSO algorithm that includes the cluster validity measure to automatically determine the true number of the cluster centers, and then to extract real cluster centers and to make a good classification.
The second task of this dissertation is to develop an evolutional fuzzy particle swarm optimization (FPSO) learning algorithm to automatically extract the near-optimum codebook of vector quantization (VQ) for carrying on image compression. Based on the adaptive learning scheme of the PSO and the flexible membership function of the fuzzy inference system, the dissertation also demonstrates the advance of the FPSOVQ-based image compression system.
The last issue of this dissertation is focuses on the topic of radial basis function networks (RBFNs) learning. An innovative hybrid recursive particle swarm optimization (HRPSO) learning algorithm with normalized fuzzy c-mean (NFCM) clustering is proposed to generate radial basis function networks (RBFNs) modeling system with small numbers of descriptive radial basis functions (RBFs) for fast approximating two complex and nonlinear functions.
論文目次 Contents

1 Introduction
1.1 Motivation…………………………………………1
1.2 Objectives…………………………………………2
1.3 Thesis Outline……………………………2

2 Literature Review
2.1 Optimization Problems…………………………5
2.2 Optimization Algorithms……………………..7
2.3 Genetic Algorithms……………………………..8
2.4 Simulated Annealing……………………………13
2.5 Particle Swarm Optimization……………….16

3 Problem Definition
3.1 The Clustering Problem………………………24
3.1.1 Definitions………….……………………..24
3.1.2 Distance and Similarity…………………..25
3.1.3 Clustering Methods………………………..29
3.1.3.1 Hierarchical clustering………………..30
3.1.3.2 Partitional clustering………………..33
3.1.3.3 K-means clustering……………………..34
3.1.3.4 Fuzzy c-means clustering……………..35
3.1.4 Cluster Validity………….……………..37
3.2 Vector Quantization……………………40
3.2.1 Definitions and Design Problem…….. 41
3.2.2 Optimality Criteria……………………..43
3.2.3 The LBG Algorithm…….………………..44
3.3 Artificial Neural Networks……………..45
3.3.1 Modeling a Neuron………………………..45
3.3.2 Neural Models in Common Use…………..52
3.3.2.1 Multilayer perceptrons……………..52
3.3.2.2 Radial basis function networks…..56

4 Alternative KPSO-Clustering Algorithm
4.1 Introduction………………………………59
4.2 Clustering with PSO Algorithm……………61
4.2.1 Objective Function-Based Clustering…..61
4.2.2 Alternative KPSO-clustering……………..62
4.3 Simulation Results…………………………69
4.4 Conclusion…………….………………………78

5 Automatic Particle Swarm Optimization Clustering Algorithm
5.1 Introduction…………………………80
5.2 AUTO-PSO Clustering Algorithm………………82
5.3 Simulation Results…………………………91
5.4 Conclusion………………………………101

6 Evolutionary Fuzzy Particle Swarm Optimization Vector Quantization Learning Scheme in Image Compression
6.1 Introduction…………………………104
6.2 Optimal Codebook Design of VQ…………………107
6.2.1 VQ Preliminaries…………………………..107
6.2.2 Fuzzy Particle Swarm Optimization Vector Quantization Design …110
6.3 Illustrated Examples…………………………120
6.4 Conclusion…………………………………130

7 Hybrid Recursive Particle Swarm Optimization Learning Algorithm in The Design of Radial Basis Function Networks
7.1 Introduction…………………………………131
7.2 RBFNs Architecture………………………134
7.3 Fuzzy Clustering………………………136
7.4 Illustrated Examples……………………146
7.5 Conclusion…………………………………151

8 Conclusions
8.1 Summary of Conclusions…………………152
8.2 Future Research. ………………………154


References………………………………………156

Publications…………………………………167
IVList
of Figures
Figure 2.1 Example of global minimizer s as well as a local minimizer s*. ..………….6
Figure 2.2 Examples of binary encoding. ……………………………………………… 10
Figure 2.3 Roulette-Wheel Selection. ………………………………………………….11
Figure 2.4 A single point crossover. …………………………………………………12
Figure 2.5 Two points crossover. ……………………………………………………12
Figure 2.6 Mutation operation. …………………….…..……………………………..13
Figure 2.7 Pseudo-code of the standard GAs. ……………………………………….13
Figure 2.8 Pseudo-code of the SA. ……………………………………………………16
Figure 2.9 Graphical representation of PSO formula. …………………………………20
Figure 2.10 Pseudo-code of the PSO algorithm. ………..……………..………………21
Figure 3.1 The difference between Manhattan distance and Euclidean distance. …..…..27
Figure 3.2 Examples of distance functions. (a) Euclidean distance, (b) Manhattan distance,
(c) Minkowski distance (p = 5), (d) Minkowski distance (p = 200). …….28
Figure 3.3 A dendogram for hierarchical clustering. ……..…………………………31
Figure 3.4 The relationship between divisive and agglomerative hierarchical clustering
algorithms. …………………………………………………………...32
Figure 3.5 K-means clustering algorithm. ……………………………………………..35
Figure 3.6 Cell regions. The codevectors are shown with “
Vparameter
= 3. (b) A two-dimensional sigmoidal RBF with center vector = [2,2]
and smoothing parameter = 3. ………………..………………………..57
Figure 3.14 Architecture of Radial basis function network. ……………………………57
Figure 4.1 The encoding of the single particle in the PSO initial population. ……….63
Figure 4.2 The distance measure plot for the alternative metric with different Beta. …..65
Figure 4.3 (a) A two-dimensional data set, (b) Distance function of alternative metric, (c)
Distance function of Euclidean norm. ………………….……………66
Figure 4.4 (a) The data set used in Example 1. The clustering results achieved by the (b)
K-means, (c) Fuzzy c-means, (d) AKPSO. ……….…………………….70
Figure 4.5 (a) The data set used in Example 2. The clustering results achieved by the (b)
K-means, (c) Fuzzy c-means, (d) AKPSO. …………………………….71
Figure 4.6 (a) The data set used in Example 3. The clustering results achieved by the (b)
K-means, (c) Fuzzy c-means, (d) AKPSO. ………………………..…….72
Figure 4.7 (a) The three-dimensional plot for the four-dimensional Iris data which are iris
setosa (○), iris versicolor (△), and iris virginica (+). The clustering results
achieved by the (b) K-means, (c) Fuzzy c-means, (d) AKPSO. ……..…73
Figure 4.7 (e) The proposed algorithm with and without one step of K-means algorithm (by
using IRIS data), where the population size is taken to be 40. ………74
Figure 4.8 (a) The data set used in Example 5. The clustering results achieved by the (b)
K-means, (c) Fuzzy c-means, (d) AKPSO. ……………………………..75
Figure 4.9 (a) The data set containing three spherical clusters with different sizes. The
clustering results achieved by the (b) K-means, (c) Fuzzy c-means, (d)
AKPSO. ………………………………………………………………76
Figure 4.10 (a) The data set used in Example 7. (b) The clustering result achieved by
K-means, where the cluster centers being [(0.4838, 0.3822, 0.2222), (1.5070,
0.4489, 0.6027)]. (c) The clustering result achieved by Fuzzy c-means, where
the cluster centers being [(0.5491, 0.3608, 0.1063), (1.3690, 0.4874, 0.7590)].
(d) The clustering result achieved by AKPSO, where the cluster centers being
[(0.9890, 0.5760, 1.0000), (0.7073, 0.3129, 0.0000)]. …………………77
Figure 5.1 Response of the average computation for special condition [(4.48, -0.0528), (3.0,
1.0), (0.8817, 3.1866)]. …………………………………………………87
-VIFigure
5.2 Response of the K-means algorithm for special condition [(4.48, -0.0528), (3.0,
1.0), (0.8817, 3.1866)]. ………………………………………………….….88
Figure 5.3 Response of the traditional PSO-clustering method in Example 1. (a) Data set
used in Example 1, (b) Performance measure of different K (K = 2, 3, … ,10)
with the traditional PSO-clustering method. ……………………………..92
Figure 5.4 Response of AUTO-PSO algorithm in Example 1. (a) Fitness value against
generation with Gbest (solid), average Pbest (dash) and average particles
(dash-dotted), (b) CS measure against generation for Gbest , (c) Final selected
Gbest , where ‘∆’is disabled and ‘○’is active, (d)The optimal classification
result by the selected cluster centers. ………………………………………94
Figure 5.5 Fitness curve with different population size. ………………………………95
Figure 5.6 Response of AUTO-PSO algorithm in Example 2. (a) The data set used in
Example 2, (b) Final Gbest , where ‘∆’is disabled and ‘○’is active, (c) The
optimal classification result by the selected cluster centers. …………….96
Figure 5.7 Response of AUTO-PSO algorithm in Example 3. (a) The data set used in
Example 3, (b) Final Gbest , where ‘∆’is disabled and ‘○’is active, (c) The
optimal classification result by the selected cluster centers. …………….98
Figure 5.8 Response of AUTO-PSO algorithm in Example 4. (a) The three-dimensional
plot for the four-dimensional IRIS data, (b) The three-dimensional plot for the
four-dimensional IRIS data: IRIS setosa (○), IRIS versicolor (△), and IRIS
virginica (+), (c) The clustering results achieved by the proposed method. ...100
Figure 5.9(a) Training images data set. ……………………………………………….101
Figure 5.9(b) Clustering result by the proposed method. ……………………………..101
Figure 6.1 385 data points distribution and contour drawing with Euclidean measure
metric. …………………………………………………………………..110
Figure 6.2 385 data points distribution and contour drawing with the proposed fuzzy
partition metric. ……………………………………………………….113
Figure 6.3 The flow chart of the fuzzy particle swarm optimization vector quantization in
the design of image compressed system. …………………………………118
Figure 6.4 Original training images. (a) Lena, (b)Peppers. ………………..………..121
Figure 6.5 PSNR in dB versus the size of the codebook for (a) “Lena”and (b)
-VII-
“Peppers”. ……………………………………………………………….. 123
Figure 6.6 Zoom-in comparison of the Lena Image. (a) Zoomed image of ‘Lena’, (b)
FPSOVQ reconstructed image of Lena (M = 128, PSNR = 34.0536 dB), (c)
LBG reconstructed image of Lena (M = 128, PSNR = 31.8366 dB), (d)
FPSOVQ reconstructed image of Lena (M = 64, PSNR = 32.3117 dB), (e) LBG
reconstructed image of Lena (M = 64, PSNR = 30.4540 dB). …………125
Figure 6.7 Zoom-in comparison of the Peppers Image. (a) Zoomed image of ‘Peppers’, (b)
FPSOVQ reconstructed image of Peppers (M = 128, PSNR = 32.6646 dB), (c)
LBG reconstructed image of Peppers (M = 128, PSNR = 31.3953 dB), (d)
FPSOVQ reconstructed image of Peppers (M = 64, PSNR = 31.4145 dB), (e)
LBG reconstructed image of Peppers (M = 64, PSNR = 29.3923 dB). ……126
Figure 6.8 Testing results with Lena image. (a) A256x256 Lena image, (b) Histogram from
original Lena image, (c) FPSOVQ reconstructed image of Lena (M = 256,
PSNR = 35.5636), (d) Histogram from FPSOVQ reconstructed image, (e) LBG
reconstructed image of Lena (M = 256, PSNR = 32.6289), (f) Histogram from
LBG reconstructed image. …………………………………………………128
Figure 6.9 Testing results with Peppers image. (a) A 256x256 Peppers image, (b)
Histogram from original Peppers Image, (c) FPSOVQ reconstructed image of
Peppers (M = 256, PSNR = 35.3088), (d) Histogram from FPSOVQ
reconstructed image, (e) LBG reconstructed image of Peppers (M = 256,
PSNR = 32.0223), (f) Histogram from LBG reconstructed image. ……….129
Figure 7.1. The proposed architecture of the RBFNs. ………………….………..135
Figure 7.2. Examples of distance functions. (a) Euclidean distance (for spherical cluster),
(b) the proposed distance (for spherical cluster), (c) Euclidean distance (for
ellipsoidal cluster), (d) the proposed distance (for ellipsoidal cluster). ....139
Figure 7.3 Simulations comparison for FCM and NFCM methods. ……………….141
Figure 7.4 Learning diagram of the RBFNMS. …………………………………….145
Figure 7.5 ) sin( ) sin( 2 1 x x
(c) Output by HRPSO, (d) fitness value against iteration in PSO and HRPSO
method. …………………………………………………………………150IXList
of Tables
Table 3.1 Activation functions commonly used in artificial neuron structure. ……….48
Table 4.1 Comparison of K-means, Fuzzy c-means, and AKPSO. ……………………….79
Table 5.1 The selected Gbest for Example 1. …………………..…………………….95
Table 5.2 The selected Gbest for Example 2. ……….……………………………….97
Table 5.3 The selected Gbest for Example 3. ……..…..…..…………………………..99
Table 6.1 Performance (PSNR) comparisons between FPSOVQ and LBG (codebook
sizes=4-256). ………………………………………………………….124
Table 7.1 Clustering results for FCM and NFCM. ………………………………….142
Table 7.2 Parameter selection by RPSO for Example 1. ………………………….148
Table 7.3 Performance comparisons with different methods. The last two rows are from ref.
[105]. ………………………………………………………………………148
Table 7.4 Parameter values by RPSO for Example 2. …………………….………151
Table 7.5 Performance comparisons with different methods for Example 2. ………151
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