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21 March 2003 Mathematical Foundation of Association Rules: mining generalized associations by linear inequalities
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Associations (not necessarily in rule forms) as patterns in data are critically analyzed. We build theory based only on what data says, and no other implicit assumptions. Data mining is regarded as a deductive science: First, we observe that isomorphic relations have isomorphic associations. Somewhat a surprise, such a simple observation turns out to have far reaching consequences. It implies that associations are properties of an isomorphic class, not an individual relation. A similar conclusion can be made for probability theory based on item counting, hence it is not adequate to characterize the "interesting-ness," since the latter one is a property of an individual relation. As a by-product of this analysis, we find that all generalized associations can be found by simply solving a set of integral linear inequalities - this is a very striking result. Finally, we observe that from the structure of the relation lattice, we may conclude that random sampling may loose substantial information about patterns.
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Tsau Young Lin and Hugo Shi "Mathematical Foundation of Association Rules: mining generalized associations by linear inequalities", Proc. SPIE 5098, Data Mining and Knowledge Discovery: Theory, Tools, and Technology V, (21 March 2003);

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