A branch & bound algorithm to determine optimal bivariate splits for oblique decision tree induction

Abstract Univariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due their major benefit being easy interpret. However, these trees only consider a single attribute per node, they often get quite large which lowers explanatory value. Oblique building algorithms, divide feature space by multidimensional hyperplanes, produce much smaller but individual splits are hard Moreover, effort finding optimal oblique is high that heuristics have applied determine local solutions. In this work, we introduce an effective branch bound procedure global bivariate concave impurity measures. Decision based on remain fairly interpretable restriction two attributes split. The resulting significantly more accurate than univariate counterparts ability adapting better underlying data capturing interactions pairs. our evaluation shows algorithm even outperforms algorithms heuristically obtained multivariate despite fact focusing only.