M-ary Random Forest - A new multidimensional partitioning approach to Random Forest

Abstract

Random Forest (RF) is composed of decision trees as base classifiers. In general, a decision tree recursively partitions the feature space into two disjoint subspaces using a single feature as axis-parallel splits for each internal node. The oblique decision tree uses a linear combination of features (to form a hyperplane) to partition the feature space in two subspaces. The later approach is an NP-hard problem to compute the best-suited hyperplane. In this work, we propose to use multiple features at a node for splitting the data as in axis parallel method. Each feature independently divides into two subspaces and this process is done by multiple features at one node. Hence, the given space is divided into multiple subspaces simultaneously, and in turn, to construct the M-ary trees. Hence, the forest formed is named as M-ary Random Forest (MaRF). To measure the performance of the task in MaRF, we have extended the notion of tree strength of the regression tree. We empirically prove that the performance of the MaRF improves due to the improvement in the strength of the M-ary trees. We have shown the performance to wide range of datasets ranging from UCI datasets, Hyperspectral dataset, MNIST dataset, Caltech 101 and Caltech 256 datasets. The efficiency of the MaRF approach is found satisfactory as compared to state-of-the-art methods.