TY - GEN

T1 - Logical analysis of data with decomposable structures

AU - Ono, Hirotaka

AU - Makino, Kazuhisa

AU - Ibaraki, Toshihide

N1 - Funding Information:
This work was partially supported by the Scienti0c Grant-in-Aid by the Ministry of Education, Science, Sports and Culture of Japan. The authors thank the anonymous referee for their helpful comments which improved the presentation of this paper.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-44968-x_39

DO - 10.1007/3-540-44968-x_39

M3 - Conference contribution

AN - SCOPUS:84949473307

SN - 3540677879

SN - 9783540677871

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 396

EP - 406

BT - Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings

A2 - Du, Ding-Zhu

A2 - Eades, Peter

A2 - Estivill-Castro, Vladimir

A2 - Lin, Xuemin

A2 - Sharma, Arun

PB - Springer Verlag

T2 - 6th Annual International Conference on Computing and Combinatorics, COCOON 2000

Y2 - 26 July 2000 through 28 July 2000

ER -