臺灣博碩士論文加值系統

Krishnapuram and Keller 於1993年提出可能性c-均值(Possibilistic c-means, PCM)演算法，藉由鬆綁模糊c-均值(Fuzzy c-means, FCM)演算法中資料點隸屬各類的隸屬度總和為1的限制，使離群值的影響力變小，群心的估計值更為穩健，因此，若配合適當的起始值和參數值，PCM會是一個尋找眾數的好方法，然而適當的起始值之選取以及必須給定群數仍舊是PCM演算法的兩大難題。在本篇論文中，我們利用PCM演算法中，若給定過多群心會發生群心重疊的現象，我們提出了一個穩健式聚類演算法，利用群心重疊的性質，且為避免起始群心之選取問題，使用所有資料點當起始群心，採合併相近群之方式，根據資料自身結構得到不錯的分類結果，我們提出了一套穩健式聚類演算法稱之為自動合併可能性聚類法(Automatic merging　possibilistic clustering method, AM-PCM)。

Krishnapuram and Keller (1993) first proposed a possibilistic approach to clustering, called possibilistic c-means (PCM), by relaxing the constraint in fuzzy c-means (FCM) that the memberships of a data point across classes sum to 1. The PCM algorithm has a tendency to produce coincident clusters. This can be a merit of PCM as a good mode-seeking algorithm if initials and parameters are suitably chosen. However, the performance of PCM heavily depends on the selection of parameters and initializations. In this paper, for solving these parameters and initializations selection problems, we propose a new scheme of PCM, called an automatic merging possibilistic clustering method (AM-PCM). The proposed AM-PCM algorithm first uses all data points as initial prototypes and then automatically merges these surrounding points around each cluster mode such that it can self-organize data groups according to the original data structure.

Abstract (Chinese) Ⅰ
Abstract (English) Ⅱ
List of Figures Ⅳ
List of Tables Ⅴ
Chapter 1. Introduction 1
Chapter 2. Three C-means Clustering Algorithms 3
2.1 Hard C-means clustering algorithm (HCM) 4
2.2 Fuzzy C-means clustering algorithm (FCM) 4
2.3 Possibilistic C-means clustering algorithm (PCM) 5
2.4 PCM as a mode-seeking algorithm 8
Chapter 3. A Robust Possibilistic Clustering Algorithm 12
3.1 The proposed algorithm 12
3.2 The computational complexity 19
3.3 A recommendation for initial D(0) for numerical data 19
3.4 For gray level image process 20
3.5 For large sample size process 21
3.6 For categorical data process 21
Chapter 4. Experimental Examples 23
Chapter 5. Conclusions and Discussions 38
References 39
Appendix A 41
Appendix B 43

[1]A. Baraldi and P. Blonda, “A survey of fuzzy clustering algorithms for pattern recognition-part I and II”, IEEE Trans. Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 29, pp. 778-801, 1999.
[2]M. Barni, V. Cappellini, and A. Mecocci, “Comments on ‘A Possibilistic Approach to Clustering,’” IEEE Trans. Fuzzy Systems, vol. 4, pp. 393-396, Aug. 1996.
[3]J.C. Bezdek, “Cluster validity with fuzzy sets,” J. Cybernet., vol. 3, pp. 58-73, 1974.
[4]J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum Press, 1981.
[5]C.L. Blake and C.J. Merz, UCI repository of machine learning databases, a huge collection of artificial and real-world data sets, 1998. Availabe from: <http://www.ics.uci.edu/ sim mlearn/MLRepository.html>.
[6]R.N. Dave, “Validating fuzzy partition obtained through c-shells clustering,” Pattern Recognition Letters, vol. 17, pp. 613-623, 1996.
[7]J.C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters,” J. Cybernetics, vol. 3, pp. 32-57, 1974.
[8]E. Forgy, “Cluster analysis of multivariate data: Efficiency vs. interpretability of classifications,” Biometrics, vol. 21, pp. 768–780, 1965.
[9]H. Frigui and R. Krishnapuram, “A Robust Competitive Clustering Algorithm With Applications in Computer Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol.21, pp. 450-465, 1999.
[10]Y. Fukuyama and M. Sugeno, “A new method of choosing the number of clusters for the fuzzy c-means method,” Proceeding of 5th Fuzzy Syst. Symp., pp. 247-250, 1989.
[11]I. Gath and A.B. Geva, “Unsupervised optimal fuzzy clustering,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol.11, pp. 73-781, 1989.
[12]D. E. Gustafson and W. C. Kessel, “Fuzzy clustering with a fuzzy covariance matrix,” Proc. IEEE CDC, San Diego, California, pp. 761-766, 1979.
[13]F. Hoppner, F. Klawonn, R. Kruse and T. Runkler, Fuzzy Cluster Analysis: Methods for Classification Data Analysis and Image Recognition. New York: Wiley, 1999.
[14]R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Trans. Fuzzy Systems, vol.1, pp. 98-110, 1993.
[15]R. Krishnapuram, H. Frigui and O. Nasraoui, “Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation- Part 1 & 2,” IEEE Trans. Fuzzy Systems, vol. 3, pp. 29-60, 1995.
[16]R. Krishnapuram and J. M. Keller, “The Possibilistic C-Means Algorithm: Insights and recommendations,” IEEE Trans. Fuzzy Systems, vol. 4, pp. 385-393, Aug. 1996.
[17]A. A. Lubischew, “On the Use of Discriminant Functions in Taxonomy,” Biometrics, vol. 18, pp. 455-477, 1962.
[18]J. MacQueen, “Some methods for classification and analysis of multivariate observations,” in Proc. 5th Berkeley Symp., vol. 1, pp. 281-297, 1967.
[19]N. R. Pal, K. Pal, J. M. Keller, and J. C. Bezdek, “A Possibilistic Fuzzy c-Means Clustering Algorithm,” IEEE Trans. Fuzzy Systems, vol. 13, pp. 517-530, 2005.
[20]T.A. Runkler and J.C. Bezdek, “Alternating cluster estimation: A new tool for clustering and function approximation,” IEEE Trans. Fuzzy Systems, vol. 7, pp. 377-393, 1999.
[21]N. Ueda, R. Nakano, Z. Ghahramani, and G. E. Hinton, “SMEM Algorithm for Mixture Models,” Neural Computation, vol. 12, pp. 2109-2128, 2000.
[22]X.L. Xie and G. Beni, “A validity measure for fuzzy clustering,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol.13, pp. 841-847, 1991.
[23]M.S. Yang, “A survey of fuzzy clustering,”Mathematical and Computer Modeling, vol. 18, pp. 1-16, 1993.
[24]M.S. Yang, Y.H. Chiang, C.C. Chen, and C.Y. Lai, “A fuzzy k-partitions model for categorical data and its comparison to the GoM model,” Fuzzy Sets and Systems, Vol.159 , pp. 390-405, 2008.
[25]M.S. Yang, Y.J. Hu, K.C.R. Lin and C.C.L. Lin, “Segmentation techniques for tissue differentiation in MRI of Ophthalmology using fuzzy clustering algorithms”, Magnetic Resonance Imaging 20, pp. 173-179, 2002.
[26]J. Yu and M.S. Yang, “A generalized fuzzy clustering regularization model with optimality tests and model complexity analysis,” IEEE Trans. Fuzzy Systems, vol. 15, pp. 904-915, 2007.
[27]L.A. Zadeh, “Fuzzy sets,” Inform. and Control, vol. 8, pp. 338-353, 1965.
[28]J. S. Zhang and Y. W. Leung, “Improved Possibilistic C-Means Clustering Algorithms,” IEEE Trans. Fuzzy Systems, vol. 12, pp. 209-217, 2004.