Practical Approximation of Optimal Multivariate Discretization

Abstract

Discretization of the value range of a numerical feature is a common task in data mining and machine learning. Optimal multivariate discretization is in general computationally intractable. We have proposed approximation algorithms with performance guarantees for training error minimization by axis-parallel hyperplanes. This work studies their efficiency and practicability. We give efficient implementations to both greedy set covering and linear programming approximation of optimal multivariate discretization. We also contrast the algorithms empirically to an efficient heuristic discretization method.