Multi-way set enumeration in weight tensors

Elisabeth Georgii*, Koji Tsuda, Bernhard Schölkopf

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

16 Citations (Scopus)


The analysis of n-ary relations receives attention in many different fields, for instance biology, web mining, and social studies. In the basic setting, there are n sets of instances, and each observation associates n instances, one from each set. A common approach to explore these n-way data is the search for n-set patterns, the n-way equivalent of itemsets. More precisely, an n-set pattern consists of specific subsets of the n instance sets such that all possible associations between the corresponding instances are observed in the data. In contrast, traditional itemset mining approaches consider only two-way data, namely items versus transactions. The n-set patterns provide a higher-level view of the data, revealing associative relationships between groups of instances. Here, we generalize this approach in two respects. First, we tolerate missing observations to a certain degree, that means we are also interested in n-sets where most (although not all) of the possible associations have been recorded in the data. Second, we take association weights into account. In fact, we propose a method to enumerate all n-sets that satisfy a minimum threshold with respect to the average association weight. Technically, we solve the enumeration task using a reverse search strategy, which allows for effective pruning of the search space. In addition, our algorithm provides a ranking of the solutions and can consider further constraints. We show experimental results on artificial and real-world datasets from different domains.

Original languageEnglish
Pages (from-to)123-155
Number of pages33
JournalMachine Learning
Issue number2
Publication statusPublished - Feb 2011
MoE publication typeA1 Journal article-refereed


  • Dense pattern enumeration
  • Graph mining
  • Multi-way set
  • N-ary relation
  • Quasi-hyper-clique
  • Tensor

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