博碩士論文 etd-0814110-125518 詳細資訊


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姓名 饒旻宗(Min-Zong Rau) 電子郵件信箱 m973010009@student.nsysu.edu.tw
畢業系所 電機工程學系研究所(Electrical Engineering)
畢業學位 碩士(Master) 畢業時期 98學年第2學期
論文名稱(中) 結合主成分分析的模糊分群法
論文名稱(英) Fuzzy Clustering with Principal Component Analysis
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    摘要(中) 在本論文中,我們結合基於相似度模糊分群法(similarity-based fuzzy clustering, SFC)與主成分分析(principal component analysis, PCA)的優點提出一系列新的分群演算法,這些新的分群演算法可以找出超球體(hyper-spherical)、超橢圓體(hyper-ellipsoidal)與斜角超橢圓體(oblique hyper-ellipsoidal)形狀的群聚。這些形狀的群聚是屬於凸(convex)形狀的群聚,透過多個多個局部凸(local convex)的群聚可以組合出一個非凸(non-convex)的群聚,意即,我們所提之分群演算法所找出的群聚更能符合資料型態。
    由於我們所使用的模糊分群演算法是屬於一種漸進式分群演算法,資料輸入順序與參數設定可能導致群聚數量過多與分群結果不穩定等問題,為了解決這兩個問題,我們又提出“重新分配”(re-assign)和 “改進的群聚合併”(modified cluster merge)演算法。前者是為了讓群聚更加穩定,而後者則是用來減少群聚數量,應用此兩種演算法達到群聚資料穩定以及群聚數量減少的效果。
    在實驗中設計出多種不同形狀的合成資料,實驗結果顯示,斜角超橢圓體形狀的群聚更能符合各種資料分佈,我們的方法能以更少的群聚達到不錯的結果。
    摘要(英) We propose a clustering algorithm which incorporates a similarity-based fuzzy clustering and principal component analysis. The proposed algorithm is capable of discovering clusters with hyper-spherical, hyperellipsoidal, or oblique hyper-ellipsoidal shapes. Besides, the number of the clusters need not be specified in advance by the user. For a given dataset, the orientation, locations, and the number of clusters obtained can truthfully reflect the characteristics of the dataset. Experimental results, obtained by running on datasets generated synthetically, show that our method performs better than other methods.
    關鍵字(中)
  • 斜橢圓群聚
  • 主成分分析
  • 模糊相似度分群
  • 漸進式分群
  • 關鍵字(英)
  • incremental clustering
  • principal component analysis
  • fuzzy clustering
  • oblique hyper-ellipsoidal cluster
  • 論文目次 摘要 i
    Abstract ii
    圖目錄 iv
    表目錄 vi
    第一章 簡介 1
    1.1 目的 4
    1.2 符號說明 5
    第二章 文獻探討 6
    2.1 基於相似度模糊分群法 6
    2.1.1 群聚產生與更新 6
    2.1.2 群聚合併 14
    2.2 主成分分析 20
    2.3 K-means 22
    2.4 Neural Gas 22
    2.5 Kernel K-means 23
    第三章 研究方法 24
    3.1 基本想法 24
    3.2 基於主成分相似度模糊分群法 25
    3.2.1 群聚合併 35
    3.2.2 即時群聚合併 42
    3.3 基於相似度模糊分群法後執行局部主成分分析 49
    3.4 重新分配 50
    3.5 實驗架構 51
    第四章 實驗與結果 52
    4.1 資料集介紹 52
    4.2 實驗一 55
    4.2.1 參數說明 55
    4.2.2 實驗結果 56
    4.3 實驗二 60
    4.3.1 參數說明 60
    4.3.2 實驗結果 60
    4.4 實驗三 70
    4.4.1 參數說明 70
    4.4.2 實驗結果 70
    4.4.3 實驗結果總結 81
    4.5 實驗四 83
    4.5.1 比較其他不同演算法 84
    第五章 結論與未來研究方向 92
    5.1 結論 92
    5.2 未來研究方向 92
    參考文獻 94
    附錄A 3.11公式推導 96
    附錄B 3.21公式推導 97
    參考文獻 [1] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algoritms, Springer, New York, 1981.
    [2] T. Kohonen, Self-organizing Maps, Springer, New York, 1995.
    [3] T. M. Martinetz, S. G. Berkovich, and K. J. Schulten, “Neural-Gas” Network for Vector Quantization and Its Application to Time-Series Prediction”, IEEE Transactions on Neural Networks, Vol. 4, No. 4, pp. 558-569, 1993.
    [4] H. Frigui and R. Krishnapuram, “A Robust Competitive Clustering Algorithm with Applications in Computer Vision”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 21, No. 5, pp. 450-465, May 1999.
    [5] F. Hoeppner, “Fuzzy Shell Clustering Algorithms in Image Processing: Fuzzy C-rectangular and 2-rectangular Shells”, IEEE Transactions on Fuzzy Systems, Vol. 5, No. 4, pp. 599-613, November 1997.
    [6] T. Kohonen, S. Kaski, K. Lagus, J. Salojarvi, V. Paatero, and A. Saarela, “Self Organization of a Massive Document Collection”, IEEE Transactions on Neural Networks, Vol. 11, No. 3, pp. 574-585, May 2000.
    [7] S. J. Lee and C. S. Ouyang, “A Neuro-fuzzy System Modeling with Self-constructing Rule Generation and Hybrid SVD-based Learning”, IEEE Transactions on Fuzzy Systems, Vol. 11, No. 3, pp. 341-353, June 2003.
    [8] W. Li, L. Jaroszewski, and A. Godzik, “Clustering of Highly Homologous Sequences to Reduce the Size of Large Protein Databases”, Bioinformatics, Vol. 17, No. 3, pp. 282-283, March 2001.
    [9] J. B. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations”, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, University of California Press, No. 1, pp. 281-297, 1967.
    [10] C. S. Ouyang, W. J. Lee, and S. J. Lee, “A TSKtype Neuro-fuzzy Network Approach to System Modeling Problems”, IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, Vol. 35, No. 4, pp. 751-767, August 2005.
    [11] K. Pearson, “On Lines and Planes of Closest Fit to Systems of Points in Space”, Philosophical Magazine, Vol. 2, No. 6, pp. 559-572, 1901.
    [12] P. Scheunders, “A Comparison of Clustering Algorithms Applied to Color Image Quantization”, Pattern Recognition Letters, Vol. 18, No. 11-13, pp. 1379-1384, November 1997.
    [13] Y. Xu, V. Olman, and D. Xu, “Clustering Gene Expression Data Using Graph-theoretic Approach: An Application of Minimum Spanning Trees”, Bioinformatics, Vol. 18, No. 4, pp. 536-545, 2002.
    [14] H. A. Boubacar, S. Lecoeuche, and S. Maouche, “SAKM: Self-adaptive Kernel Machine A Kernel-based Algorithm for Online Clustering”, Neural Networks, Vol. 21, No. 9, pp. 1287-1301, 2008.
    [15] B. Schölkopf, J. Platt, J. Shawe-Taylor, A. J. Smola, and R. C. Williamson, “Estimating the Support of a High-dimensional Distribution”, Neural Computation, Vol. 13, No. 7, pp. 1443-1471, 2001.
    [16] H. Hotelling, “Analysis of a Complex of Statistical Variables into Principal Components”, Journal of Educational Psychology, Vol. 24, pp. 417-441, 1933.
    [17] R. Möller, and H. Hoffmann, “An Extension of Neural Gas to Local PCA”, Neurocomputing, Vol. 62, pp. 305-326, 2004.
    [18] D. Huang, Z. Yi, and X. Pu, “A New Local PCA-SOM Algorithm”, Neurocomputing, Vol. 71, pp. 3544-3552, 2008.
    [19] K. Y. Lee, “Local Fuzzy PCA Based GMM with Dimension Reduction on Speaker Identification”, Pattern Recognition Letters, Vol. 25, pp. 1811-1817, 2004.
    口試委員
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  • 李錫智 - 指導教授
  • 口試日期 2010-07-21 繳交日期 2010-08-14

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