Logical analysis of data with decomposable structures

Hirotaka Ono; Kazuhisa Makino; Toshihide Ibaraki

doi:10.1007/3-540-44968-x_39

Logical analysis of data with decomposable structures

Hirotaka Ono, Kazuhisa Makino, Toshihide Ibaraki

mathematics and information

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to nd relations among attributes are considered important. In this paper, given a data set (T;F) of a phenomenon, where T ⊆{0,1}ⁿ 1gn denotes a set of positive examples and F ⊆{0,1}ⁿdenotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. Such information will reveal hierarchical structure of the phenomenon under consideration. We rst study computational complexity of the problem of nding decomposable Boolean extensions. Since the problem turns out to be intractable (i.e., NP-complete), we propose a heuristic algorithm in the second half of the paper. Our method searches a decomposable partition of the set of all attributes, by using the error sizes of almost-t decomposable extensions as a guiding measure, and then nds structural relations among the attributes in the obtained partition. The results of numerical experiment on synthetically generated data sets are also reported.

Original language	English
Title of host publication	Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings
Editors	Ding-Zhu Du, Peter Eades, Vladimir Estivill-Castro, Xuemin Lin, Arun Sharma
Publisher	Springer Verlag
Pages	396-406
Number of pages	11
ISBN (Print)	3540677879, 9783540677871
DOIs	https://doi.org/10.1007/3-540-44968-x_39
Publication status	Published - 2000
Event	6th Annual International Conference on Computing and Combinatorics, COCOON 2000 - Sydney, Australia Duration: Jul 26 2000 → Jul 28 2000

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1858
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	6th Annual International Conference on Computing and Combinatorics, COCOON 2000
Country	Australia
City	Sydney
Period	7/26/00 → 7/28/00

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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Ono, H., Makino, K., & Ibaraki, T. (2000). Logical analysis of data with decomposable structures. In D-Z. Du, P. Eades, V. Estivill-Castro, X. Lin, & A. Sharma (Eds.), Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings (pp. 396-406). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1858). Springer Verlag. https://doi.org/10.1007/3-540-44968-x_39

Logical analysis of data with decomposable structures. / Ono, Hirotaka; Makino, Kazuhisa; Ibaraki, Toshihide.

Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings. ed. / Ding-Zhu Du; Peter Eades; Vladimir Estivill-Castro; Xuemin Lin; Arun Sharma. Springer Verlag, 2000. p. 396-406 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1858).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ono, H, Makino, K & Ibaraki, T 2000, Logical analysis of data with decomposable structures. in D-Z Du, P Eades, V Estivill-Castro, X Lin & A Sharma (eds), Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1858, Springer Verlag, pp. 396-406, 6th Annual International Conference on Computing and Combinatorics, COCOON 2000, Sydney, Australia, 7/26/00. https://doi.org/10.1007/3-540-44968-x_39

Ono H, Makino K, Ibaraki T. Logical analysis of data with decomposable structures. In Du D-Z, Eades P, Estivill-Castro V, Lin X, Sharma A, editors, Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings. Springer Verlag. 2000. p. 396-406. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-44968-x_39

Ono, Hirotaka ; Makino, Kazuhisa ; Ibaraki, Toshihide. / Logical analysis of data with decomposable structures. Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings. editor / Ding-Zhu Du ; Peter Eades ; Vladimir Estivill-Castro ; Xuemin Lin ; Arun Sharma. Springer Verlag, 2000. pp. 396-406 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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