### 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}^{n}denotes 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 |
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Title of host publication | Computing and Combinatorics - 6th Annual International Conference, COCOON 2000, Proceedings |

Editors | Peter Eades, Vladimir Estivill-Castro, Xuemin Lin, Arun Sharma, Ding-Zhu Du |

Publisher | Springer Verlag |

Pages | 396-406 |

Number of pages | 11 |

ISBN (Print) | 3540677879, 9783540677871 |

Publication status | Published - Jan 1 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) |
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Volume | 1858 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th Annual International Conference on Computing and Combinatorics, COCOON 2000 |
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Country | Australia |

City | Sydney |

Period | 7/26/00 → 7/28/00 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

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

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

*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.

}

TY - GEN

T1 - Logical analysis of data with decomposable structures

AU - Ono, Hirotaka

AU - Makino, Kazuhisa

AU - Ibaraki, Toshihide

PY - 2000/1/1

Y1 - 2000/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84949473307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949473307&partnerID=8YFLogxK

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 - Eades, Peter

A2 - Estivill-Castro, Vladimir

A2 - Lin, Xuemin

A2 - Sharma, Arun

A2 - Du, Ding-Zhu

PB - Springer Verlag

ER -