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We propose a novel algorithm for optimizing multivariate linear thresholdfunctions as split functions of decision trees to create improved Random Forestclassifiers. Standard tree induction methods resort to sampling and exhaustivesearch to find good univariate split functions. In contrast, our methodcomputes a linear combination of the features at each node, and optimizes theparameters of the linear combination (oblique) split functions by adopting avariant of latent variable SVM formulation. We develop a convex-concave upperbound on the classification loss for a one-level decision tree, and optimizethe bound by stochastic gradient descent at each internal node of the tree.Forests of up to 1000 Continuously Optimized Oblique (CO2) decision trees arecreated, which significantly outperform Random Forest with univariate splitsand previous techniques for constructing oblique trees. Experimental resultsare reported on multi-class classification benchmarks and on Labeled Faces inthe Wild (LFW) dataset.

CO2 Forest: Improved Random Forest by Continuous Optimization of Oblique Splits