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

Authors:
Endre Boros;Vladimir Menkov
Affiliations:
RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854-8003, USA;Aqsaqal Enterprises, Penticton, British Columbia, Canada
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

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 F(l"1(x),l"2(x)), where l"1(x) and l"2(x) are linear functions of binary variables x@?{0,1}^n, and F:R^2@?R. Though this problem is NP-hard, in general, an optimal solution x^* 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 x^@e, for any given @e0, such that F(l"1(x^*),l"2(x^*))-F(l"1(x^@e),l"2(x^@e))