A bottom-up oblique decision tree induction algorithm

Decision tree induction algorithms are widely used in knowledge discovery and data mining, specially in scenarios where model comprehensibility is desired. A variation of the traditional univariate approach is the so-called oblique decision tree, which allows multivariate tests in its non-terminal nodes. Oblique decision trees can model decision boundaries that are oblique to the attribute axes, whereas univariate trees can only perform axis-parallel splits. The majority of the oblique and univariate decision tree induction algorithms perform a top-down strategy for growing the tree, relying on an impurity-based measure for splitting nodes. In this paper, we propose a novel bottom-up algorithm for inducing oblique trees named BUTIA. It does not require an impurity-measure for dividing nodes, since we know a priori the data resulting from each split. For generating the splitting hyperplanes, our algorithm implements a support vector machine solution, and a clustering algorithm is used for generating the initial leaves. We compare BUTIA to traditional univariate and oblique decision tree algorithms, C4.5, CART, OC1 and FT, as well as to a standard SVM implementation, using real gene expression benchmark data. Experimental results show the effectiveness of the proposed approach in several cases.