A complete gradient clustering algorithm formed with kernel estimators

Piotr Kulczycki; Małgorzata Charytanowicz

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 1, page 123-134
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Piotr Kulczycki, and Małgorzata Charytanowicz. "A complete gradient clustering algorithm formed with kernel estimators." International Journal of Applied Mathematics and Computer Science 20.1 (2010): 123-134. <http://eudml.org/doc/207968>.

@article{PiotrKulczycki2010,
abstract = {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.},
author = {Piotr Kulczycki, Małgorzata Charytanowicz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {data analysis and mining; clustering; gradient procedures; nonparametric statistical methods; kernel estimators; numerical calculations},
language = {eng},
number = {1},
pages = {123-134},
title = {A complete gradient clustering algorithm formed with kernel estimators},
url = {http://eudml.org/doc/207968},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Piotr Kulczycki
AU - Małgorzata Charytanowicz
TI - A complete gradient clustering algorithm formed with kernel estimators
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 1
SP - 123
EP - 134
AB - 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.
LA - eng
KW - data analysis and mining; clustering; gradient procedures; nonparametric statistical methods; kernel estimators; numerical calculations
UR - http://eudml.org/doc/207968
ER -

References

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Citations in EuDML Documents

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  1. Witold Andrzejewski, Artur Gramacki, Jarosław Gramacki, Graphics processing units in acceleration of bandwidth selection for kernel density estimation
  2. Adam Nowicki, Michał Grochowski, Kazimierz Duzinkiewicz, Data-driven models for fault detection using kernel PCA: A water distribution system case study
  3. Anna Fabijańska, Tomasz Węgliński, Krzysztof Zakrzewski, Emilia Nowosławska, Assessment of hydrocephalus in children based on digital image processing and analysis
  4. Piotr Kulczycki, Szymon Łukasik, An algorithm for reducing the dimension and size of a sample for data exploration procedures

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