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2010 | 20 | 1 | 123-134
Tytuł artykułu

A complete gradient clustering algorithm formed with kernel estimators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to provide a gradient clustering algorithm in its complete form, suitable for direct use without requiring a deeper statistical knowledge. The values of all parameters are effectively calculated using optimizing procedures. Moreover, an illustrative analysis of the meaning of particular parameters is shown, followed by the effects resulting from possible modifications with respect to their primarily assigned optimal values. The proposed algorithm does not demand strict assumptions regarding the desired number of clusters, which allows the obtained number to be better suited to a real data structure. Moreover, a feature specific to it is the possibility to influence the proportion between the number of clusters in areas where data elements are dense as opposed to their sparse regions. Finally, the algorithm-by the detection of oneelement clusters-allows identifying atypical elements, which enables their elimination or possible designation to bigger clusters, thus increasing the homogeneity of the data set.
Rocznik
Tom
20
Numer
1
Strony
123-134
Opis fizyczny
Daty
wydano
2010
otrzymano
2008-10-02
poprawiono
2009-04-10
Twórcy
  • Systems Research Institute, Center for Stochastic Data Analysis Methods, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
  • Department of Automatic Control and Information Technology, Faculty of Electrical and Computer Engineering, Cracow University of Technology, ul. Warszawska 24, 31-155 Cracow, Poland
  • Systems Research Institute, Center for Stochastic Data Analysis Methods, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
  • Institute of Mathematics and Computer Science, John Paul II Catholic University of Lublin, ul. Konstantynów 1 H, 20-708 Lublin, Poland
Bibliografia
  • Anderberg, M. R. (1973). Cluster Analysis for Applications, Academic Press, New York, NY.
  • Barnett, V. and Lewis, T. (1994). Outliers in Statistical Data, Wiley, Chichester.
  • Carreira-Perpinan, M. A. (2006). Fast nonparametric clustering with gaussian blurring mean-shift, Proceedings of the International Conference on Machine Learning, Pittsburgh, PA, USA, pp. 153-160.
  • Cheng, Y. (1995). Mean shift, mode seeking, and clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 17(8): 790-799.
  • Comaniciu, D. and Meer, P. (2002). Mean shift: A robust approach toward feature space analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence 24(5): 603-619.
  • Daniel, K. (2009). Marketing strategy support method for a cell phone operator, Ph.D. thesis, Systems Research Institute, Polish Academy of Sciences, Warsaw, (in Polish).
  • Everitt, B. S., Landau, S. and Leese, M. (2001). Cluster Analysis, Arnold, London.
  • Fukunaga, K. and Hostetler, L. D. (1975). The estimation of the gradient of a density function, with applications in pattern recognition, IEEE Transactions on Information Theory 21(1): 32-40.
  • Girolami, M. and He, C. (2003). Probability density estimation from optimally condensed data samples, IEEE Transactions on Pattern Analysis and Machine Intelligence 25(10): 1253-1264.
  • Jain, A. K. and Dubes, R. C. (1988). Algorithms for Clustering Data, Prentice Hall, Englewood Cliffs, NJ.
  • Kincaid, D. and Cheney, W. (2002). Numerical Analysis, Brooks/Cole, Pacific Grove, CA.
  • Kulczycki, P. (2005). Kernel Estimators in Systems Analysis, WNT, Warsaw, (in Polish).
  • Kulczycki, P. (2007). Kernel estimators in systems research, in P. Kulczycki, O. Hryniewicz and J. Kacprzyk (Eds), Information Technologies in Systems Research, WNT, Warsaw, pp. 79-105, (in Polish).
  • Kulczycki, P. (2008). Kernel estimators in industrial applications, in B. Prasad (Ed.), Soft Computing Applications in Industry, Springer-Verlag, Berlin, pp. 69-91.
  • Kulczycki, P. and Charytanowicz, M. (2008). A complete gradient clustering algorithm, in K. Malinowski and L. Rutkowski (Eds), Control and Automation: Current Problems and Their Solutions, EXIT, Warsaw, pp. 312-321, (in Polish).
  • Kulczycki, P. and Daniel, K. (2009). A method for supporting the marketing strategy of a mobile phone network provider, Przegląd Statystyczny 56(2): 116-134, (in Polish).
  • Kulczycki, P. and Łukasik, S. (2009). Reduction of sample dimension and size for synthesis of a statistical fault detection system, in Z. Kowalczuk (Ed.), Systems Detecting, Analysing and Tolerating Faults, PWNT, Gdańsk, pp. 139-146, (in Polish).
  • Larose, D. T. (2006). Data Mining Methods and Models, Wiley, New York, NY.
  • Lubischew, A. A. (1962). On the use of discriminant functions in taxonomy, Biometrics 18(4): 455-478.
  • Muller, H. G. (1984). Smooth optimum kernel estimators of densities, regression curves and models, The Annals of Statistics 12(2): 766-774.
  • Pal, S. K. and Mitra, P. (2004). Pattern Recognition Algorithms for Data Mining, Chapman and Hall, London.
  • Rodriguez, R. and Suarez, A. G. (2006). A new algorithm for image segmentation by using iteratively the mean shift filtering, Scientific Research and Essay 1(2): 43-48.
  • Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
  • Wand, M. P. and Jones, M. C. (1994). Kernel Smoothing, Chapman and Hall, London.
  • Wang, W. J., Tan, Y. X., Jiang, J. H., Lu, J. Z., Shen, G. L. and Yu, R. Q. (2004). Clustering based on kernel density estimation: Nearest local maximum searching algorithm, Chemometrics and Intelligent Laboratory Systems 72(1): 1-8.
  • Yang, C., Duraiswami, R., DeMenthon, D. and Davis, L. (2003). Mean-shift analysis using quasi-newton methods, Proceedings of the IEEE International Conference on Image Processing, Barcelona, Spain, pp. 447-450.
  • Zhang, K., Tang, M. and Kwok, J. T. (2005). Applying neighborhood consistency for fast clustering and kernel density estimation, Proceedings of the IEEE International Conference on Vision and Pattern Recognition, San Diego, CA, USA, pp. 1001-1007.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i1p123bwm
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