Exponentially Scaled Point Processes and Data Classification

0430516 - ÚI 2015 RIV GR eng C - Konferenční příspěvek (zahraniční konf.)
Jiřina, Marcel
Exponentially Scaled Point Processes and Data Classification.
Advances in Applied and Pure Mathematics. Proceedings of the 2014 International Conference on Pure Mathematics, Applied Mathematics, Computational Methods PMAMCM 2014. Athens: WSEAS Press, 2014 - (Mastorakis, N.; Pardalos, P.; Agarwal, R.; Kočinac, L.), s. 179-185. Mathematics and Computers in Science and Engineering Series, 29. ISBN 978-1-61804-240-8. ISSN 2227-4588.
[PMAMCM 2014. Santorini Island (GR), 17.07.2014-21.07.2014]
Grant CEP: GA MŠMT(CZ) LG12020
Institucionální podpora: RVO:67985807
Klíčová slova: multivariate data * nearest neighbor * Erlang distribution * multifractal * scaling exponent * classification * IINC
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum

We use a measure for distances of neighbors’ of a given point that is based on lp metrics and a scaling exponent. We show that if the measure scales with scaling exponent mentioned, then distribution function of this measure converges to Erlang distribution. The scaling of distances is used for design of a classifier. Three variants of classifier are described. The local approach uses local value of scaling exponent. The global method uses the correlation dimension as the scaling exponent. In the IINC method indexes of neighbors of the query point are essential. Results of some experiments are shown and open problems of classification with scaling are discussed.
Trvalý link: http://hdl.handle.net/11104/0235422