Random forest of perfect trees: concept, performance, applications and perspectives

Motivation: The principle of Breiman's random forest (RF) is to build and assemble complementary classification trees in a way that maximizes their variability. We propose a new type of random forest that disobeys Breiman's principles and involves building trees with no classification errors in very large quantities. We used a new type of decision tree that uses a neuron at each node as well as an in-innovative half Christmas tree structure. With these new RFs, we developed a score, based on a family of ten new statistical information criteria, called Nguyen information criteria (NICs), to evaluate the predictive qualities of features in three dimensions. Results: The first NIC allowed the Akaike information criterion to be minimized more quickly than data obtained with the Gini index when the features were introduced in a logistic regression model. The selected features based on the NICScore showed a slight advantage compared to the support vector machines-recursive feature elimination (SVM-RFE) method. We demonstrate that the inclusion of artificial neurons in tree nodes allows a large number of classifiers in the same node to be taken into account simultaneously and results in perfect trees without classification errors.

Automated summary

A new type of random forest was proposed, deviating from Breiman's principles, by building trees with no classification errors in large quantities, using decision trees with neurons at each node and a unique structure. A family of statistical information criteria called Nguyen information criteria (NICs) was developed to evaluate the predictive qualities of features, showing advantages over traditional methods like Akaike information criterion and support vector machines-recursive feature elimination (SVM-RFE). The inclusion of artificial neurons in tree nodes allowed for the consideration of a large number of classifiers simultaneously, resulting in perfect trees without classification errors.