Abstract
Transactional data are ubiquitous. Several methods, including frequent itemset mining and co-clustering, have been proposed to analyze transactional databases. In this work, we propose a new research problem to succinctly summarize transactional databases. Solving this problem requires linking the high level structure of the database to a potentially huge number of frequent itemsets. We formulate this problem as a set covering problem using overlapped hyperrectangles (a concept generally regarded as tile according to some existing papers); we then prove that this problem and its several variations are NP-hard, and we further reveal its relationship with the compact representation of a directed bipartite graph. We develop an approximation algorithm Hyper which can achieve a logarithmic approximation ratio in polynomial time. We propose a pruning strategy that can significantly speed up the processing of our algorithm, and we also propose an efficient algorithm Hyper+ to further summarize the set of hyperrectangles by allowing false positive conditions. Additionally, we show that hyperrectangles generated by our algorithms can be properly visualized. A detailed study using both real and synthetic datasets shows the effectiveness and efficiency of our approaches in summarizing transactional databases.
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Responsible editor: Bart Goethals.
A preliminary version of this article appeared in Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (Xiang et al. 2008). This submission has substantially extended the previous paper and contains new and major-value added contribution in comparison with the conference publication.
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Xiang, Y., Jin, R., Fuhry, D. et al. Summarizing transactional databases with overlapped hyperrectangles. Data Min Knowl Disc 23, 215–251 (2011). https://doi.org/10.1007/s10618-010-0203-9
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DOI: https://doi.org/10.1007/s10618-010-0203-9