Oblique random forests with binary and ternary decision structures and non-parallel hyperplanes classifiers

Due to their robust nature, ensemble methods have gained a lot of popularity these days. In this work, we propose several variations of oblique decision tree ensembles called as oblique random forests, which are implemented with binary and ternary decision structures. Oblique random forests are trained using a linear classifier, where the feature axis is not invariably orthogonal to the decision hyperplanes at each internal node of the base model. For the multiclass classification problems, the training samples are partitioned at non-leaf nodes into groups of classes corresponding to the underlying geometric characteristics, with respect to a randomly chosen feature subspace. Each of the proposed models employ a different binary base classifier. The binary classifiers used for this work are twin support vector machines (TWSVM), Improvements on nu-TWSVM, multi-surface proximal support vector machine (MPSVM) and Regularized MPSVM. We also propose a novel approach to choose the final hyperplane to split the data at the non-leaf node while optimizing an impurity criterion in the decision tree. This work presents a comparative analysis of different base classifiers for implementing Oblique Random forests using binary and ternary decision structures. In addition, multiple regularization strategies like Tikhonov regularization, axis-parallel split regularization, and null space regularization are used to address limited sample size issues in the oblique random forest decision trees implemented with MPSVM and RegMPSVM. Whereas implementations for TWSVM and I nu TWSVM is done with Tikhonov regularization only. All these models are compared for their generalization ability through benchmark 38 UCI classification datasets. The efficacy of these methods is also established through statistical analysis.