Data mining is defined as the process of discovering significant and potentially useful patterns in large volumes of data. Discovering associations between items in a large database is one such data mining activity. In finding associations, support is used as an indicator as to whether an association is interesting. In this paper, we discuss three alternative interest measures for associations: any-confidence, all-confidence, and bond. We prove that the important downward closure property applies to both all-confidence and bond. We show that downward closure does not hold for any-confidence. We also prove that, if associations have a minimum allconfidence or minimum bond, then those associations will have a given lower bound on their minimum support and the rules produced from those associations will have a given lower bound on their minimum confidence as well. However, associations that have that minimum support (and likewise their rules that have minimum confidence) may not satisfy the minimum all-confidence or minimum bond constraint. We describe the algorithms that efficiently find all associations with a minimum all-confidence or minimum bond and present some experimental results.

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