### Abstract

We consider the problem of finding two-dimensional association rules for categorical attributes. Suppose we have two conditional attributes A and B both of whose domains are categorical, and one binary target attribute whose domain is {“positive”, “negative”}. We want to split the Cartesian product of domains of A and B into two subsets so that a certain objective function is optimized, i.e., we want to find a good segmentation of the domains of A and B. We consider in this paper the objective function that maximizes the confidence under the constraint of the upper bound of the support size. We first prove that the problem is NP-hard, and then propose an approximation algorithm based on semidefinite programming. In order to evaluate the effectiveness and efficiency of the proposed algorithm, we carry out computational ex- periments for problem instances generated by real sales data consisting of attributes whose domain size is a few hundreds at maximum. Approxi- mation ratios of the solutions obtained measured by comparing solutions for semidefinite programming relaxation range from 76% to 95%. It is observed that the performance of generated association rules are signifi- cantly superior to that of one-dimensional rules.

Original language | English |
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Title of host publication | Discovery Science - 2nd International Conference, DS 1999, Proceedings |

Editors | Setsuo Arikawa, Koichi Furukawa |

Publisher | Springer-Verlag |

Pages | 148-159 |

Number of pages | 12 |

ISBN (Print) | 354066713X, 9783540667131 |

DOIs | |

Publication status | Published - 1999 Jan 1 |

Event | 2nd International Conference on Discovery Science, DS 1999 - Tokyo, Japan Duration: 1999 Dec 6 → 1999 Dec 8 |

### 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 | 1721 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd International Conference on Discovery Science, DS 1999 |
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Country | Japan |

City | Tokyo |

Period | 99/12/6 → 99/12/8 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Discovery Science - 2nd International Conference, DS 1999, Proceedings*(pp. 148-159). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1721). Springer-Verlag. https://doi.org/10.1007/3-540-46846-3_14