TY - GEN

T1 - Approximation of optimal two-dimensional association rules for categorical attributes using semidefinite programming

AU - Fujisawa, Katsuki

AU - Hamuro, Yukinobu

AU - Katoh, Naoki

AU - Tokuyama, Takeshi

AU - Yada, Katsutoshi

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-46846-3_14

DO - 10.1007/3-540-46846-3_14

M3 - Conference contribution

AN - SCOPUS:73349106769

SN - 354066713X

SN - 9783540667131

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

SP - 148

EP - 159

BT - Discovery Science - 2nd International Conference, DS 1999, Proceedings

A2 - Arikawa, Setsuo

A2 - Furukawa, Koichi

PB - Springer Verlag

T2 - 2nd International Conference on Discovery Science, DS 1999

Y2 - 6 December 1999 through 8 December 1999

ER -