On the Inverse Frequent Itemset Mining Problem for Condensed Representations of Itemsets

Abstract

Inverse frequent itemset mining can be successfully modelled as an instance of the Probabilistic Satisfiability problem. Given a transaction database we can perform a frequent itemset mining algorithm, like the Apriori algorithm, to obtain useful itemset collections such as frequent or closed itemsets. We then use these itemset collections as frequency constraints in order to reconstruct the original database by solving a linear programming problem. There are cases however, where the reconstructed database is not in direct agreement with the original one. In this study, we analyse the degree of similarity between the original database and the reconstructed one, when different variations of condensed itemset representations are used as the initial frequency constraints. We examine how much the initial database properties and itemset relations have been preserved when we emphasize on the frequent itemset border and assess database quality by measuring database distance metrics. As this solution framework presents increased computational cost, we also consider a heuristic approach that is based on the notion that a transaction can be also considered as an itemset and compare the strengths and weaknesses of each framework when the same conditions apply. We manage to improve the efficiency of existing heuristic based approaches to the problem by utilizing smaller initial itemset collections. Our work contributes in (a) privacy preserving data mining and (b) gain in transaction database storage memory savings.