Analytical Split Value Calculation for Numerical Attributes in Hoeffding Trees with Misclassification-Based Impurity

Hoeffding tree is a method to incrementally build decision trees. A common approach to handle numerical attributes in Hoeffding trees is to represent their sufficient statistics as Gaussian distributions. Our contribution in this paper is to prove that by using Gaussian distribution as sufficient statistics and misclassification error as impurity measure, there is an analytical method to exactly calculate the best splitting values. Three different approaches for using this theorem are proposed and all three are tested on both synthetic and real datasets. The experiments suggest that this approach can create smaller trees and learn faster and achieve higher accuracy in most problems. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.