Hyper-rectangular space partitioning trees: a practical approach
(2002) , 22 pages
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- Abstract
- The process of computation of classication trees can be characterized as involving three basic choices: the type of splits considered in the growing process, the criterion to be optimized at each step of the process, and the way to get right-sized trees. Most implementations are ordinary binary trees, i.e. trees whose successive cuts are made by hypeplanes perpendicular to the axes, while most of the litterature concerns the various possible criteria and pruning methods. L. Devroye, L. Gy orfy and G. Lugosi (1996) dene and consider the remarkable theoretical properties of a binary tree classier whose prominent feature is the particular type of splits used in its construction: at a given node, partitioning is made by hyper-rectangles rather than hyper-planes. We propose an approximation of the solution for the complex optimization problem involved to allow insights on the practical advantages of those trees. Then we compare the performance of our algorithm with some leading algorithms for ordinary binary trees, namely CART and C4.5 as implemented in the Splus "tree" procedure and in SAS 's Enterprise Miner respectively. For this purpose, data sets which traditionally enhance the weaknesses of classication trees are used, as well as data sets commonly used for comparisons.
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Citations
De Macq, I., & Simar, L. (2002). Hyper-rectangular space partitioning trees: a practical approach (STAT Discussion Papers 0301). https://hdl.handle.net/2078.5/34281