Finding Multivariate Splits in Decision Trees Using Function Optimization

George H. John

We present a new method for top-down induction of decision trees (TDIDT) with multivariate binary splits at the nodes. The primary contribution of this work is a new splitting criterion called soft entropy, which is continuous and differentiable with respect to the parameters of the splitting function. Using simple gradient descent to find multivariate splits and a novel pruning technique, our TDIDT-SEH (Soft Entropy Hyperplanes) algorithm is able to learn very small trees with better accuracy than competing learning algorithms on most datasets examined.

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