TY - JOUR

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.

PY - 2002/10/30

Y1 - 2002/10/30

N2 - In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to find relations among attributes are considered important. In this paper, given a data set (T,F) where T ⊆ {0,1}n denotes a set of positive examples and F⊆{0,1}n denotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. We first study computational complexity of the problem of finding 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-fit decomposable extensions as a guiding measure, and then finds structural relations among the attributes in the obtained partition. Some results of numerical experiment on randomly generated data sets are also reported.

AB - In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to find relations among attributes are considered important. In this paper, given a data set (T,F) where T ⊆ {0,1}n denotes a set of positive examples and F⊆{0,1}n denotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. We first study computational complexity of the problem of finding 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-fit decomposable extensions as a guiding measure, and then finds structural relations among the attributes in the obtained partition. Some results of numerical experiment on randomly generated data sets are also reported.

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U2 - 10.1016/S0304-3975(01)00413-3

DO - 10.1016/S0304-3975(01)00413-3

M3 - Conference article

AN - SCOPUS:0037202055

SN - 0304-3975

VL - 289

SP - 977

EP - 995

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 2

T2 - Computing and Combinatorics (COCOON 2000)

Y2 - 1 July 2000 through 1 July 2000

ER -