Abstract
In this paper we survey the main approaches to fuzzy shell cluster analysis which is simply a generalization of fuzzy cluster analysis to shell like clusters, i.e. clusters that lie in nonlinear subspaces. Therefore we introduce the main principles of fuzzy cluster analysis first. In the following we present some fuzzy shell clustering algorithms In many applications it is necessary to determine the number of clusters as well as the classification of the data set. Subsequently therefore we review the main ideas of unsupervised fuzzy shell cluster analysis. Finally we present an application of unsupervised fuzzy shell cluster analysis in computer vision.
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References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum, New York 1981.
Bock, H.H.: Classification and Clustering: Problems for the Future, in: New Approaches in Classification and Data Analysis (Ed. Diday, E., Lechevallier, Y., Schrader, M., Bertrand, P. and Burtschy, B. ), Springer, Berlin, 1994, 3–24.
Davé, R.N.: Use of the Adaptive Fuzzy Clustering Algorithm to Detect Lines in Digital Images, Proc. Intelligent Robots and Computer Vision VIII, 1192 (1989), 600–611.
Frigui, H. and Krishnapuram, R.: A Comparison of Fuzzy Shell-Clustering Methods for the Detection of Ellipses, IEEE Transactions on Fuzzy Systems, 4 (1996), 193–199.
Gath, I. and Geva, A. B.: Unsupervised Optimal Fuzzy Clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (1989), 773–781.
Gustafson, E.E. and Kessel, W.C.: Fuzzy Clustering with a Fuzzy Covariance Matrix, IEEE CDC, San Diego, Californien, 1979, 761–766.
Höppner, F., Klawonn, F. and Kruse, R.: Fuzzy-Clusteranalyse. Verfahren für die Bilderkennung, Klassifikation und Datenanalyse, Vieweg, Braunschweig 1996.
Krishnapuram, R. and Freg, C.P.: Fitting an Unknown Number of Lines and Planes to Image Data through Compatible Cluster Merging, Pattern Recognition, 25 (1992), 385–400.
Krishnapuram, R., Frigui, H. and Nasraoui, O.: The Fuzzy C Quadric Shell clustering algorithm and the detection of second-degree curves, Pattern Recognition Letters 14 (1993), 545–552.
Krishnapuram, R., Frigui, H. and Nasraoui, O.: Fuzzy and Possibilistic Shell Clustering Algorithms and Their Application to Boundary Detection and Surface Approximation Part 1 2, IEEE Transactions on Fuzzy Systems, 3 (1995), 29–60.
Krishnapuram, R. and Keller, J.: A Possibilistic Approach to Clustering, IEEE Transactions on Fuzzy Systems, 1 (1993), pp. 98–110.
Krishnapuram, R. and Keller, J.: Fuzzy and Possibilistic Clustering Methods for Computer Vision, Neural Fuzzy Sytems 12 (1994), 133–159.
Moore, J.J.: The Levenberg-Marquardt Algorithm: Implementation and Theory, in: Numerical Analysis (Ed. Watson, G.A. ), Springer, Berlin, 1977, 105–116.
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© 1997 Springer-Verlag Wien
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Klawonn, F., Kruse, R., Timm, H. (1997). Fuzzy Shell Cluster Analysis. In: Della Riccia, G., Lenz, HJ., Kruse, R. (eds) Learning, Networks and Statistics. International Centre for Mechanical Sciences, vol 382. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2668-4_7
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DOI: https://doi.org/10.1007/978-3-7091-2668-4_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82910-3
Online ISBN: 978-3-7091-2668-4
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