Induction of Quadratic Decision Trees using Genetic Algorithms and k-D Trees

Genetic Algorithm-based Quadratic Decision Tree (GA-based QDT) has been applied successfully in various classification problems with non-linear class boundaries. However, the execution time of GA-based QDT is quite long. In this paper, a new version of GA-based QDT, called Genetic Algorithm-based Quadratic Decision Tree with k-D Tree (GA-based QDT with k-D Tree), is proposed. In the proposed algorithm, a k-D tree is constructed at each non-leaf node of a decision tree to evaluate the impurity reduction due to a quadratic hypersurface. Experiments show that the proposed algorithm is faster than GA-based QDT on datasets with lower dimensionality or the number of training samples is sufficiently large, without sacrificing the quality of a quadratic decision tree. Although the Gini index is used to measure the impurity of a set of samples, various impurity measures including entropy and the Twoing value can also be used in the proposed algorithm. Key-Words: Decision Trees, Genetic Algorithms, k-D Trees, Quadratic Hypersurface, Impurity, Data Mining