Quantitative Association Rules Based on Half-Spaces: An Optimization Approach

We tackle the problem of finding association rules for quantitative data. Whereas most of the previous approaches operate on hyperrectangles, we propose a representation based on half-spaces. Consequently, the left-hand side and right-hand side of an association rule does not contain a conjunction of items or intervals, but a weighted sum of variables tested against a threshold. Since the downward closure property does not hold for such rules, we propose an optimization setting for finding locally optimal rules. A simple gradient descent algorithm optimizes a parameterized score function, where iterations optimizing the first separating hyperplane alternate with iterations optimizing the second. Experiments with two real-world data sets show that the approach finds non-random patterns and scales up well. We therefore propose quantitative association rules based on half-spaces as an interesting new class of patterns with a high potential for applications.