Abstract

In this paper we present a new multivariate decision tree algorithm LMDT, which combines linear machines with decision trees. LMDT constructs each test in a decision tree by training a linear machine and then eliminating irrelevant and noisy variables in a controlled manner. To examine LMDT's ability to find good generalizations we present results for a variety of domains. We compare LMDT empirically to a univariate decision tree algorithm and observe that when multivariate tests are the appropriate bias for a given data set, LMDT finds small accurate trees. 1 Introduction One commonly used approach for learning from examples is to induce a univariate decision tree (Hunt, Marin & Stone, 1966; Breiman, Friedman, Olshen & Stone, 1984; Quinlan, 1986). Each test in a univariate tree is based on one of the input variables and therefore, is restricted to representing a split through the instance space that is orthogonal to the variable's axis. Such a bias may be inappropriate for problems...

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