A Study of Strength and Correlation in Random Forests

In this paper we present a study on the Random Forest (RF) family of classification methods, and more particularly on two important properties called strength and correlation. These two properties have been introduced by Brennan in the calculation of an upper bound of the generalization error. We thus propose to experimentally study the actual relation between these properties and the error rate in order to confirm and extend the Breiman theoretical results. We show that the error rate statistically decreases with the joint maximization of the strength and minimization of the correlation, and this for different sizes of RF.