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This paper presents a new hybrid fuzzy clustering method. In the proposed method, cluster prototypes are values that minimize the introduced generalized cost function. The proposed method can be considered as a generalization of fuzzy c–means (FCM) method as well as the fuzzy c–median (FCMed) clustering method. The generalization of the cluster cost function is made by applying the Lp norm. The values that minimize the proposed cost function have been chosen as the group prototypes. The weighted myriad is the special case of the group prototype, when the Lp norm is the L2 (Euclidean) norm. The cluster prototypes are the weighted meridians for the L1 norm. Artificial data set is used to demonstrate the performance of proposed method.
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Tom
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69--76
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Bibliogr. 16 poz., rys., tab.
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- Silesian University of Technology, Institute of Electronics, Akademicka 16, 44-100 Gliwice, Poland
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Bibliografia
- [1] ARCE G.R., KALLURI S., Fast algorithm for weighted myriad computation by fixed point search, IEEE Transactions on Signal Processing, Vol. 48, 2000, pp. 159–171.
- [2] ARCE G.R., KALLURI S., Robust frequency-selective filtering using weighted myriad filters admitting real-valued weights, IEEE Transactions on Signal Processing, Vol. 49, 2001, pp. 2721–2733.
- [3] AYSAL T.C., BARNER K.E., Meridian filtering for robust signal processing, IEEE Transactions on Signal Processing, Vol. 55, 2007, pp. 3949–3962.
- [4] BEZDEK, J.C., Pattern recognition with fuzzy objective function algorithms, Published by Plenum Press in New York, 1981.
- [5] CHATZIS S., VARVARIGOU Th., Robust fuzzy clustering using mixtures of Student’s-t distributions, Pattern Recognition Letters, Vol. 29, 2008, pp.1901–1905.
- [6] DAVE R.N., KRISHNAPURAM R., Robust clustering methods: a unified view, IEEE Transactions on Fuzzy Systems, Vol. 5, 1997, pp. 270–293.
- [7] FRIGUI H., KRISHNAPURAM R., A robust competitive clustering algorithm with application in computer vision, IEEE Transaction On Pattern Analysis and Machine Intelligence, Vol. 21, 1999, pp. 450–465.
- [8] HATHAWAY R.J., BEZDEK J.C., HU Y., Generalized fuzzy c-means clustering strategies using Lp norm distances, IEEE Transactions on Fuzzy Systems, Vol.8, 2000, pp. 576–582.
- [9] HUBER P., Robust statistics, Published by Wiley in New York, 1981.
- [10] KAUFMAN L., ROUSSEEUW P., Finding groups in data, Published by Wiley-Interscience, 1990.
- [11] KERSTEN P.R., Fuzzy order statistics and their application to fuzzy clustering, IEEE Transactions on Fuzzy Systems, Vol. 7, 1999, pp. 708–712.
- [12] KRISHNAPURAM R., KELLER J.M., A possibilistic approach to clustering, IEEE Transactions on Fuzzy Systems, Vol. 1, 1993, pp. 98–110.
- [13] KRISHNAPURAM R., KELLER J.M., The possibilistic c-means algorithm: insights and recommendations, IEEE Transactions on Fuzzy Systems, Vol. 4, 1996, pp. 385–396.
- [14] PEDRYCZ W., Knowledge-based clustering, Published by Wiley-Interscience, 2005.
- [15] PRZYBYŁA T., Fuzzy c-myriad clustering method, System Modeling Control, 2005, pp. 249–254.
- [16] PRZYBYŁA T., JEŻEWSKI J., HOROBA K., The adaptive fuzzy meridian and its application to fuzzy clustering, Advances in Intelligent and Soft Computing, Vol. 51, 2009, pp. 247–256.
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Bibliografia
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bwmeta1.element.baztech-article-PWA4-0018-0008