系統識別號 | U0002-2505200615111100 |
---|---|
DOI | 10.6846/TKU.2006.01162 |
論文名稱(中文) | 粒子群演算法為基礎的演化式學習-系統設計及其應用 |
論文名稱(英文) | PSO-Based Evolutionary Learning : System Design and Applications |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 電機工程學系博士班 |
系所名稱(英文) | Department of Electrical and Computer Engineering |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 94 |
學期 | 2 |
出版年 | 95 |
研究生(中文) | 陳慶逸 |
研究生(英文) | Ching-Yi Chen |
學號 | 891350018 |
學位類別 | 博士 |
語言別 | 英文 |
第二語言別 | |
口試日期 | 2006-05-19 |
論文頁數 | 169頁 |
口試委員 |
指導教授
-
余繁(fyee@mail.tku.edu.tw)
委員 - 蘇木春 委員 - 許獻聰 委員 - 詹益光 委員 - 翁慶昌 |
關鍵字(中) |
粒子群演算法 群聚分析 群聚驗證 向量量化 類神經網路 |
關鍵字(英) |
Particle Swarm Optimization Cluster analysis Cluster Validity Vector Quantization Fuzzy c-means Neural Networks |
第三語言關鍵字 | |
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. |
第三語言摘要 | |
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 |
參考文獻 |
REFERENCES [1] R. Rardin, Optimization in Operations Research, Prentice Hall, New Jersey, USA, 1998. [2] F. Van den Bergh and A. P. Engelbrecht, “A New Locally Convergent Particle Swarm Optimizer,” Proceedings of the IEEE Conference on Systems, Man and Cybernetics, Hammamet, Tunisia, 2002. [3] M. Omran, Particle Swarm Optimization Methods for Pattern Recognition and Image Processing, Ph.D. Thesis, University of Pretoria, 2004. [4] P. Pardalos, A. Migdalas, and R. Burkard, Combinatorial and Global Optimization, World Scientific Publishing Company, 2002. [5] K. Demirciler, Contributions to Efficient Vector Quantization and Frequency Assignment Design and Implementation, Ph.D. Thesis, University of Southern California, 2003. [6] D. G. Luenberger, Linear and Nonlinear Programming, Addison–Wesley Publishing Company, 1984. [7] Y. Shang, Global Search Methods for Solving Nonlinear Optimization Problems, Ph.D. Thesis, University of Illinois, 1997. [8] Z. Michalewicz and D. Fogel, How to Solve it: Modern Heuristics, Springer-Verlag, Berlin, 2000. [9] P. Van Laarhoven and E. Aarts, Simulated Annealing: Theory and Applications, Kluwer Academic Publishers, 1987. [10] S. Kirkpatric, C. D. Gellat, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science, Vol. 220, pp. 671-680, 1983. [11] M. Duque-Anton, D. Kunz, and B. Ruber, “Channel assignment for Cellular Radio using Simulated Annealing,” IEEE Trans. on Vehicular Technology, Vol. 42, No. 1, pp.14-21, 1993. [12] F. Glover, “Tabu Search – Part I,” ORSA Journal on Computing, Vol. 1, No. 3, pp. 190-206, 1989. [13] J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, University of Michigan Press, Ann Arbor, MI, USA, 1975. [14] T. Back, “Evolutionary Algorithm: Comparisons of Approaches,” Computing with Biological Metaphors, Chapman and Hall, Cambridge, UK, 1994. [15] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, 1996. [16] E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial and Neural Computing, Interscience series in discrete mathematics and optimization, John Wiley & Sons, New York, 1989. [17] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” Journal of Chemical Physics, Vol. 21, pp. 1087 – 1092, 1953. [18] C. W. Gardiner, Handbook of Stochastic Methods, Berlin, Springer, 1983. [19] M. Lundy and A. Mees, “Convergence of an Annealing Algorithm,” Mathematical Programmming, Vol. 34, pp. 111-124, 1986. [20] S. Kirkpatrick, “Optimization by Simulated Annealing: Quantitative Studies,” Journal of Statistical Physics, Vol. 34, pp. 975-986, 1984. [21] J. Kennedy and R. Eberhart, "Particle Swarm Optimization," Proceedings of the IEEE International Conference on Neural Networks (ICNN), Vol. IV, Perth, Australia, pp.1942-1948, 1995. [22] R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp.39-43, 1995. [23] R. Eberhart and Y. Shi, “Particle Swarm Optimization: Developments, Applications and Resources,” Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2001), Seoul, Korea, 2001. [24] Y. Shi and R. Eberhart, “Parameter Selection in Particle Swarm Optimization. Evolutionary Programming VII,” Proceedings of EP 98, pp.591-600, 1998. [25] X. Hu, PSO Tutorial, http://www.cems.uwe.ac.uk/~jsmith/ci/pso/tutorials.php.htm (visited May 2006). [26] R. Battiti, M. Brunato, and S. Pasupuleti, Do not be afraid of local minima: Affine Shaker and Particle Swarm, Technical Report, pp.8-13, May 2005. [27] Y. Shi and R. Eberhart, “A modied particle swarm optimizer,” Proceedings of the IEEE Congress on Evolutionary Computation (CEC 1998), Piscataway, NJ, pp. 69-73, 1998. [28] J. Kennedy and R. Eberhart, Swarm Intelligence, Morgan Kaufmann Publishers, 2001. [29] M. Clerc, “The swarm and the queen: towards a deterministic and adaptive particle swarm optimization,” Proceedings of the IEEE Congress on Evolutionary Computation, Washington, DC, Piscataway, NJ: IEEE Service Center, pp 1951-1957, 1999. [30] M. Clerc and J. Kennedy, “The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space,” IEEE Trans. on Evolutionary Computation, Vol. 6, pp. 58-73, 2002. [31] Y. Shi, “Particle Swarm Optimization,” IEEE Neural Networks Society, Feb. 2004. [32] S. Thodoridis, K. Koutroumbas, Pattern Recognition, Academic Press, San Diego, 1999. [33] R. N. Dave and R. Krishnapuram, “Robust clustering methods: a united view,” IEEE Trans. on Fuzzy Systems, Vol. 5, No. 2, pp.270-293, 1997. [34] X. L. Xie and G. Beni, “A validity measure for fuzzy clustering,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 13, No. 8, pp. 841-847, 1991. [35] G. Hamerly, Learning Structure and Concepts in Data using Data Clustering, Ph.D. Thesis, University of California, San Diego, 2003. [36] G. Hamerly and C. Elkan, “Alternatives to the K-means Algorithm that Find Better Clusterings,” Proceedings of the ACM Conference on Information and Knowledge Management (CIKM-2002), pp. 600-607, 2002. [37] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1976. [38] A. Jain, M. Murty, and P. Flynn, “Data Clustering: A Review,” ACM Computing Surveys, Vol. 31, No. 3, pp.264-323, 1999. [39] C. H. Chou, The Development of Learning Mechanisms and Their Applications, Ph.D. Thesis, University of Tamkang, Taiwan, 2003. [40] A. K. Jain, M. N. Murty, and P. J. Flynn, “Data Clustering,” ACM Computing Surveys, Vol. 31, No. 3, pp.264-323, 1999. [41] R. H. Turi, Clustering-Based Colour Image Segmentation, Ph.D. Thesis, University of Monash, Australia, 2001. [42] E. Forgy, “Cluster Analysis of Multivariate Data: Efficiency versus Interpretability of Classification,” Biometrics, Vol. 21, pp.768-769, 1965. [43] J. C. Dunn, "A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters," Journal of Cybernetics, Vol. 3, No. 3, pp. 32-57, 1973. [44] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algoritms, Plenum Press, New York, 1981. [45] J. C. Bezdek and N. R. Pal, “Some new indexes for cluster validity,” IEEE Trans. on Systems, Man, and Cybernetics, Part-B, Vol.28, pp.301-315, 1998. [46] J. C. Bezdek, “Numerical taxonomy with fuzzy sets,” Journal of Mathematical Biology, Vol. 1, pp.57-71, 1974. [47] A. M. Bensaid, L. O. Hall, J. C. Bezdek, L. P. Clarke, M. L. Silbiger, J. A. Arrington, and R. F. Murtagh, “Validity-guided Clustering with applications to image segmentation,” IEEE Trans. on Fuzzy Systems, Vol. 4, No. 2, pp.112-123, 1996. [48] X. L. Xie and G. Beni, “A validity measure for fuzzy clustering,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 13, No.8, pp.841-847, 1991. [49] J. C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact, well separated clusters,” Journal of Cybernetics, Vol. 3, No. 3, pp.35-57, 1973. [50] D. L. Davies and D. W. Bouldin, “A cluster separation measure,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 1, No. 4, pp.224-227, 1979. [51] data-compression.com, Vector Quantization, http://www.data-compression.com/vq.shtml (visited Jan. 2006). [52] A. Gersho and R. M. Gray, Vector Quantization and Signal Compression, Kluwer Academic Publishers, 1992. [53] Y. Linde, A. Buzo, and R. M. Gray, “An Algorithm for Vector Quantizer Design,' IEEE Trans. on Communications, pp. 702-710, 1980. [54] N. B. Karayiannis and P. I. Pai, "Fuzzy Vector Quantization Algorithms and Their Application in Image Compression," IEEE Trans. on Image Processing, Vol. 4, pp. 1193-1201, 1995. [55] D. E. Rumelhart, G. E. Hinton, and R. J. Willimans, “Learning representations by backpropagating errors,” Nature, Vol. 323, pp.533-536, 1986. [56] C. M. Bishop, Neural Networks for Pattern Recognition, Oxford Press, 1995. [57] J. Moody and C. J. Darkin, “Fast learning in networks of locally-tuned processing units,” Neural Computation, Vol. 1, No. 2, pp. 281-294, 1989. [58] M. Powell, "Radial basis functions for multivariable interpolation: a review," Proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, pp.143-167, 1985. [59] I. Maqsood, M. R. Khan, and A. Abraham, “Intelligent weather monitoring systems using connectionist models,” Neural, Parallel and Scientific Computations, Vol. 10, pp.157-178, 2002. [60] M. J. Orr, “Regularization in the selection of radial basis function centers,” Neural Computation, Vol. 7, No.3, pp.606-623, 1995. [61] S. Z. Selim and M. A. Ismail, “K-means type algorithms: a generalized convergence theorem and characterization of local optimality,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 6, No.1, pp. 81-87, 1984. [62] L. Bottou and Y. Bengio, “Convergence properties of the K-means algorithms,” Advances in Neural Information Processing Systems, Vol.7, The MIT Press, Cambridge, MA, pp.585-592, 1995. [63] K. L. Wu and M. S. Yang, “Alternative c-means clustering algorithms,” Pattern Recognition, Vol. 35, pp. 2267-2278, 2002. [64] U. Maulik and S. Bandyopadhyay, "Genetic algorithm-based clustering technique," Pattern Recognition, Vol. 33, pp. 1455-1465, 2000. [65] J. L. R. Filho, P. C. Treleaven, and C. Alippi, “Genetic algorithm programming environments,” IEEE Trans. on Compute, Vol. 27, pp.28-43, 1994. [66] M. R. Anderberg, Cluster Analysis for Application, Academic Press, New York, 1973. [67] M. R. Garey, D. S. Johnson, and H. S. Witsenhausen, “The complexity of the generalized Lloyd-Max problem,” IEEE Trans. on Information Theory, Vol. 28, No. 2, pp.255-256, 1982. [68] C. Y. Chen and F. Ye, “Particle Swarm Optimization Algorithm and Its Application to Clustering Analysis,” Proceedings of the IEEE International Conference on Networking, Sensing and Control, Taipei, Taiwan, pp.789-794, 2004. [69] C. Y. Chen and F. Ye, “K-means Algorithm Based on Particle Swarm Optimization,” Proceedings of International Conference on Informatics, Cybernetics, and Systems, I-Shou University, Taiwan, pp.1470-1475, 2003. [70] S. Bandopadhyay and U. Maulik, “Genetic Clustering for Automatic Evolution of Clusters and Application to Image Classification,” Pattern Recognition, Vol 35, pp. 1197-1208, 2002. [71] C. C. Wong and B. C. Lin, “Neighbor-based clustering algorithm,” International Journal of Electrical Engineering, Vol. 11, No.2, pp.173-181, 2004. [72] C. H. Chou, M. C. Su, and E. Lai, “A new cluster validity measure and its application to image compression,” Pattern Analysis and Applications, Vol. 7, No. 2, pp. 205-220, 2004. [73] J. C. Dunn, “Well separated clusters and optimal fuzzy partitions,” Journal of Cybernetics, Vol. 4, pp. 95-104, 1974. [74] J. T. Tou and R. C. Gonzalez, Pattern Recognition Principles, Addison-Wesley, 1974. [75] F. Ye and C. Y. Chen, “Alternative KPSO-Clustering Algorithm”, Tamkang Journal of Science and Engineering, Vol. 8, No. 2, pp. 165-174, 2005. [76] D. Feng, S. Wenkang, C. Liangzhou, D.Yong, and Z. Zhenfu, “Infrared image segmentation with 2-D maximum entropy method based on particle swarm optimization (PSO),” Pattern Recognitions Letters, Vol. 26, No. 5, pp. 597-603, 2005. [77] H. M. Feng, “Self generation fuzzy modeling systems through hierarchical recursive-based particle swarm optimization,” Cybernetics and Systems: An International Journal, Vol. 36, No. 6, pp. 623-639, 2005. [78] M. C. Su, T. K. Liu, and H. T. Chang, “An efficient initialization scheme for the self-organizing feature map Algorithm,” Proceedings of International Joint Conference on Neural Networks, Washington, DC, pp. 1906-1910, 1999. [79] K. L. Oehler and R. M. Gray, “Combining image compression and classification using vector quantization,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 17, No. 5, pp. 461-473, 1995. [80] T. Hofmann and J. M. Buhmann, “Competitive learning algorithms for robust vector quantization,” IEEE Trans. on Signal Processing, Vol. 46, No. 6, pp.1665-1675, 1998. [81] L. A. Zadeh, “Fuzzy sets,” Information and Control, Vol. 8, pp.338-353, 1965. [82] N. B. Karayiannis and P. I. Pai, “Fuzzy vector quantization algorithms and their application in image compression,” IEEE Trans. on Image Processing, Vol. 4, No. 9, pp. 1193-1201, 1995. [83] X. Kong, R.Wang, and G. Li, “Fuzzy clustering algorithms based on resolution and their application in image compression,” Pattern Recognition, Vol. 35, No. 11, pp.2439-2444, 2004. [84] W. Xu, A. K. Nandi, and J. Zhang, “Novel fuzzy reinforced learning vector quantization algorithm and its application in image compression,” IEE Proceedings-Vision, Image and Signal Processing, Vol. 150, No. 5, pp.292-28, 2003. [85] F. Pasi, “Genetic algorithm with deterministic crossover for vector quantization,” Pattern Recognition Letters, Vol. 21, No. 1, pp.61-68, 2000. [86] Y. H. Yu, C. C. Chang, and Y. C. Hu, “A genetic-based adaptive threshold selection method for dynamic path tree structured vector quantization,” Image and Vision Computing, Vol. 23, No. 6, pp.597-609, 2005. [87] C. Y. Chen, K. Y. Chen, and F. Ye, “Evolutionary-based Vector Quantizer Design,” Proceedings of International Conference on System & Signals, I-Shou University, Taiwan, pp.649-654, 2005. [88] H. Ishibuchi, T. Nakashima, and T. Morisawa, “Voting in fuzzy rule-based systems for pattern classification problems,” Fuzzy Sets and Systems, Vol. 103, pp.223-238, 1992. [89] D. F. Akhmetov, Y. Dote, and S.J. Ovaska, “Fuzzy neural network with general parameter adaptation for modeling of nonlinear time-series,” IEEE Trans. on Neural Networks, Vol. 12, No. 1, pp.148-152, 2001. [90] F. Behloul, B. P. F. Lelieveldt, A. Boudraa, and J. H. C. Reiber, “Optimal design of radial basis function neural networks for fuzzy-rule extraction in high dimensional data,” Pattern Recognition, Vol. 35, No. 3, pp.659-675, 2002. [91] S. W. Choi, D. Lee, J. H. Park, and I. B. Lee, “Nonlinear regression using RBFN with linear submodels,” Chemometrics and Intelligent Laboratory Systems, Vol. 65, No. 2, pp.191-208, 2003. [92] C. C. Chuang, J. T. Jeng, and P. T. Lin, “Annealing robust radial basis function networks for function approximation with outliers,” Neurocomputing, Vol. 56, pp.123-139, 2004. [93] O. Ciftcioghu, “GA with orthogonal transformation for RBFN configuration,” Proceeding of IEEE International Conference on Neural Networks, pp. 1934-1939, 2002. [94] J. Park and I. W. Sandberg, “Approximation and radial basis function networks,” Neural Computation, Vol. 5, pp.305-316, 1993. [95] M. D. Nam and T. C. Thanh, “Approximation of function and its derivatives using radial basis function networks,” Applied Mathematical Modeling, Vol. 27, No. 3, pp.197-220, 2003. [96] J. C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters,” Journal of Cybernetics, Vol. 3, pp.32-57, 1974. [97] Z. L. Gaing, “A Particle swarm optimization approach for optimum design of PID controller in AVR system,” IEEE Trans. on Energy Conversion, Vol. 19, No. 2, pp.384-391, 2004. [98] C. F. Juang, “A Hybrid of genetic algorithm and particle swarm optimization for recurrent network design,” IEEE Trans. on Systems, Man and Cybernetics, Vol. 34, No. 2, pp.997-1006, 2003. [99] J. Kennedy, “The particle swarm: Social adaptation of knowledge,” Proceedings of IEEE International Conference on Evolutionary Computation, Indianapolis, pp. 303-308, 1997. [100] S. Naka, T. Genji, T. Yura, and Y. Fukuyama, “A Hybrid Particle Swarm Optimization for Distribution State Estimation,” IEEE Trans. on Power Systems, Vol. 18, No. 1, pp.60-68, 2003. [101] L. X. Wang, A course in fuzzy systems and control, Prentice Hall, 1997. [102] C. C. Wong and C. C. Chen, “A GA-based method for constructing fuzzy systems directly from numerical data,” IEEE Trans. on Systems, Man and Cybernetics, Vol. 30, No. 6, pp.905-911, 2000. [103] J. S. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall, New Jersey, 1997. [104] C. C. Wong and C. C. Chen, “A hybrid clustering and gradient descent approach for fuzzy modeling,” IEEE Trans. on Systems, Man and Cybernetics, Vol. 29, pp.686-693, 1999. [105] S. J. Lee and C. H. Ouyang, “A neuro-fuzzy system modeling with self-constructing rule generation and hybrid SVD-based learning,” IEEE Trans. on Fuzzy Systems, Vol. 11, No. 3, pp.341-353, 2004. [106] M. Sugeno and T. Yasukawa, “Fuzzy-logic-based approach to qualitative modeling,” IEEE Trans. on Fuzzy Systems, Vol. 1, No. 1, pp.7-31, 1993. [107] M. Lovbjerg, Improving Particle Swarm Optimization by Hybridization of Stochastic Search Heuristics and Self-Organized Critically, Master’s Thesis, University of Aarhus, Denmark, 2002. [108] P. Angeline, “Evolutionary Optimization versus Particle Swarm Optimization: Philosophy and Performance Difference,” Proceedings of the Seventh Annual Conference on Evolutionary Programming, pp.601-610, 1998. |
論文全文使用權限 |
如有問題,歡迎洽詢!
圖書館數位資訊組 (02)2621-5656 轉 2487 或 來信