Abstract

A non-greedy approach for constructing globally optimal multivariate decision trees with fixed structure is proposed. Previous greedy tree construction algorithms are locally optimal in that they optimize some splitting criterion at each decision node, typically one node at a time. In contrast, global tree optimization explicitly considers all decisions in the tree concurrently. An iterative linear programming algorithm is used to minimize the classification error of the entire tree. Global tree optimization can be used both to construct decision trees initially and to update existing decision trees. Encouraging computational experience is reported. 1 Introduction Global Tree Optimization (GTO) is a new approach for constructing decision trees that classify two or more sets of n-dimensional points. The essential difference between this work and prior decision tree algorithms (e.g. CART [5] and ID3 [10]) is that GTO is non-greedy. For greedy algorithms, the "best" decision at each node...

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