| Approximation of Optimal Two-Dimensional Association Rules for Categorical Attributes Using Semidefinite Programming (2007) | |||||||||||||||
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 e#ectiveness and e#ciency of the proposed algorithm, we carry out computational experiments for problem instances generated by real sales data consisting of attributes whose domain size is a few hundreds at maximum. Approximation ratios of the solu... | |||||||||||||||
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