# An Algorithm for Mining Implicit Itemset Pairs Based on Differences of Correlations

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## Abstract

Given a transaction database as a global set of transactions and its local database obtained by some conditioning to the global one, we consider a pair of itemsets whose degrees of correlations are higher in the local database than in the global one. A problem of finding paired itemsets with high correlation in one database is known as Discovery of Correlation, and some algorithms to search for such characteristic paired itemsets are already proposed. However, even non-characteristic paired itemsets in the local database are also meaningful, provided the degree of correlation increases much higher in the local database than in the global one. They can be an implicit and hidden evidence showing that something particular to the local database occurs even though they are not yet realized as characteristic ones in the local. From this viewpoint, we have already proposed to measure the significance of paired itemsets by the difference of two correlations before and after the conditioning to the local database, and define a notion of DC pairs whose degrees of differences of correlations are high. As DC pairs are regarded as compound itemsets consisting of two component itemsets, we can have two basic strategies for finding them. One strategy firstly examines the compound itemsets and then the components, while another one does the component itemsets and then the compound ones. According to the former strategy, which we have already proposed and tested for its effectiveness, we have to enumerate many number of candidate compound itemsets that cannot be decomposable to components. For this reason, this paper presents a new algorithm according to the second strategy. It firstly enumerate possible component itemsets based on a new pruning rule for cutting off useless components. Secondly it forms the compound itemsets by combining the components thus detected, while we also make use of a constraint for preventing our algorithm from checking meaningless combinations.

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