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  Multi-way set enumeration in weight tensors

Georgii, E., Tsuda, K., & Schölkopf, B. (2011). Multi-way set enumeration in weight tensors. Machine Learning, 82(2), 123-155. doi:10.1007/s10994-010-5210-y.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-BC96-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0001-BCAC-A
Genre: Journal Article

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Georgii, E1, 2, Author              
Tsuda, K, Author              
Schölkopf, B1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: 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.

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 Dates: 2011-02
 Publication Status: Published in print
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 Rev. Type: -
 Identifiers: DOI: 10.1007/s10994-010-5210-y
BibTex Citekey: 6848
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Title: Machine Learning
Source Genre: Journal
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Publ. Info: Dordrecht : Springer
Pages: - Volume / Issue: 82 (2) Sequence Number: - Start / End Page: 123 - 155 Identifier: ISSN: 0885-6125
CoNE: https://pure.mpg.de/cone/journals/resource/08856125