Application of Copulas to Data Mining Based on Observational Logic

Autoři: prof. RNDr. Ing. Martin Holeňa, CSc.
Rok vydání: 2013
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: ITAT 2013: Information Technologies - Applications and Theory Workshops, Posters, and Tutorials
Projekty: Konstrukce pokročilých srozumitelných klasifikátorů
Bibliografická citace: HOLEŇA, Martin, ŠČAVNICKÝ, M. Application of Copulas to Data Mining Based on Observational Logic. In: VINAŘ, T., HOLEŇA, M., LEXA, M., PEŠKA, L., VOJTÁŠ, P., eds. ITAT 2013: Information Technologies - Applications and Theory Workshops, Posters, and Tutorials. North Charleston: CreateSpace Independent Publishing Platform, 2013, S. 77-85. ISBN 978-1-4909-5208-6.
ID: 396831

Abstrakt

The objective of the paper is a small contribution to data mining based on observational logic - introducing generalized quantifiers inspired by copulas. Fitting copulas to multidimensional data is an increasingly important method for analyzing dependencies, and the new quantifiers of observational logic assess the possibility to describe the data by a hierarchical Archimedean copula with given properties. To this end, basic concepts pertaining to copulas, Archimedean copulas and hierarchical Archimedean copulas are first recalled, together with those properties that will be needed for the definition of the new quantifiers. Since the result of assessing the possibility to describe the data by a copula depends not only on the properties of that copula, but also on the precise algorithm for fitting it to the data, we present the algorithm we have used to this end, before finally defining the new quantifiers. The paper concludes with a brief illustration of applying the proposed quantifiers to the well-known Iris data set.