Measures on Boolean polynomials and their applications in data mining

Authors:
Szymon Jaroszewicz;Dan A. Simovici;Ivo Rosenberg
Affiliations:
Department of Computer Science, University of Massachusetts at Boston, Boston, MA;Department of Computer Science, University of Massachusetts at Boston, Boston, MA;Universitè de Montréal, C.P. 6128, succ. A, Montréal, P.Q. H3C 3J7, Canada
Venue:
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Year:
2004

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Abstract

We characterize measures on free Boolean algebras and we examine the relationships that exist between measures and binary tables in relational databases. It is shown that these measures are completely defined by their values on positive conjunctions, and a formula that yields this value is obtained using the method of indicators. An extension of the notion of support that is well suited for tables with missing values is presented. Finally, we obtain Bonferroni-type inequalities that allow for approximative evaluations of these measures for several types of queries. An approximation algorithm and an analysis of the results produced is also included.