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  Multi-way set enumeration in real-valued tensors

Georgii, E., Tsuda, K., & Schölkopf, B. (2009). Multi-way set enumeration in real-valued tensors. In T. Ding, & C. Li (Eds.), Proceedings of the 2nd Workshop on Data Mining using Matrices and Tensors (DMMT 2009) (pp. 32-41). New York, NY, USA: ACM Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C495-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F901-4
Genre: Conference Paper

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 Creators:
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. An n-set pattern consists of specific subsets of the n instance sets such that all possible n- ary associations between the corresponding instances are observed. This provides 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 combinations have been recorded in the data. Second, we take association weights into account. More precisely, we propose a method to enumerate all n- sets that satisfy a minimum threshold with respect to the average association weight. Non-observed associations obtain by default a weight of zero. 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 data sets from different domains.

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 Dates: 2009-06
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1145/1581114.1581118
BibTex Citekey: 5932
 Degree: -

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Title: KDD 2009 Workshop on Data Mining using Matrices and Tensors
Place of Event: Paris, France
Start-/End Date: 2009-06-28

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Title: Proceedings of the 2nd Workshop on Data Mining using Matrices and Tensors (DMMT 2009)
Source Genre: Proceedings
 Creator(s):
Ding, T, Editor
Li, C, Editor
Affiliations:
-
Publ. Info: New York, NY, USA : ACM Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 32 - 41 Identifier: ISBN: 978-1-60558-673-1