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Concepts of a Discrete Random Variable.

Authors :
Bock, H. -H.
Gaul, W.
Vichi, M.
Arabie, Ph.
Baier, D.
Critchley, F.
Decker, R.
Diday, E.
Greenacre, M.
Lauro, C.
Meulman, J.
Monari, P.
Nishisato, S.
Ohsumi, N.
Opitz, O.
Ritter, G.
Schader, M.
Weihs, C.
Brito, Paula
Cucumel, Guy
Source :
Selected Contributions in Data Analysis & Classification; 2007, p247-258, 12p
Publication Year :
2007

Abstract

A formal concept is defined in the literature as a pair (extent, intent) with respect to a context which is usually empirical, as for example a sample of transactions. This is somewhat unsatisfying since concepts, though born from experiences, should not depend on them. In this paper we consider the above concepts as ‘empirical concepts' and we define the notion of concept, in a context-free framework, as a limit intent, by proving, applying the large number law, that : Given a random variable χ taking its value in a countable σ-semilattice, the random intents of empirical concepts, with respect to a sample of χ, converge almost everywhere to a fixed deterministic limit, called a concept, whose identification shows that it only depends on the distribution Pχ of χ. Moreover, the set of such concepts is the σ-semilattice generated by the support of χ and has even a structure of σ-lattice: the lattice concept of a random variable. We also compute the mean number of concepts and frequent itemsets for a hierarchical Bernoulli mixtures model. Last, we propose an algorithm to find out maximal frequent itemsets by using minimal winning coalitions of Pχ. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISBNs :
9783540735588
Database :
Supplemental Index
Journal :
Selected Contributions in Data Analysis & Classification
Publication Type :
Book
Accession number :
33315439
Full Text :
https://doi.org/10.1007/978-3-540-73560-1_23