Exact and approximate discrete optimization algorithms for finding useful disjunctions of categorical predicates in data analysis Original Research Article

We discuss a discrete optimization problem that arises in data analysis from the binarization of categorical attributes. It can be described as the maximization of a function image, where image and image are linear functions of binary variables image, and image. Though this problem is NP-hard, in general, an optimal solution image of it can be found, under some mild monotonicity conditions on F, in pseudo-polynomial time. We also present an approximation algorithm which finds an approximate binary solution image, for any given image, such that image, at the cost of no more than image operations. Though in general C depends on the problem instance, for the problems arising from [en]binarization of categorical variables it depends only on F, and for all functions considered we have image.