Exponentially Scaled Point Processes and Data Classification

Authors: Marcel Jiřina
Publication year: 2014
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Advances in Applied and Pure Mathematics. Proceedings of the 2014 International Conference on Pure Mathematics, Applied Mathematics, Computational Methods PMAMCM 2014
Projects: Advanced statistical analysis and non-statistical separation techniques for physical processing detection in data sets sampled by means of elementary particle accelerators.
Bibliographic citation: JIŘINA, Marcel. Exponentially Scaled Point Processes and Data Classification. In: MASTORAKIS, N.E., PARDALOS, P.M., AGARWAL, R.P., KOČINAC, L., eds. 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, S. 179-185. Mathematics and Computers in Science and Engineering Series, 29. ISBN 978-1-61804-240-8. ISSN 2227-4588.
ID: 430516

Abstract

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.