Summarizing transactional databases with overlapped hyperrectangles

  • Authors:
  • Yang Xiang;Ruoming Jin;David Fuhry;Feodor F. Dragan

  • Affiliations:
  • Department of Biomedical Informatics, The Ohio State University, Columbus, USA 43210;Department of Computer Science, Kent State University, Kent, USA 44242;Department of Computer Science and Engineering, The Ohio State University, Columbus, USA 43210;Department of Computer Science, Kent State University, Kent, USA 44242

  • Venue:
  • Data Mining and Knowledge Discovery
  • Year:
  • 2011

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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.