Approximations by Smooth Transitions in Binary Space Partitions

Abstract

This work proposes a simple approximation scheme for discrete data that leads to an infinitely smooth result without global optimization. It combines the flexibility of binary space partitions trees with the statistical robustness of smooth transition regression trees. The construction of the tree is straightforward and easily controllable, using error-driven metrics or external constraints. Moreover, it leads to a concise representation. Applications on synthetic and real data, both scalar and vector-valued demonstrated the effectiveness of this approach.