Classifying Two Class data using Hyper Rectangle Parallel to the Coordinate Axes

One of the machine learning tasks is supervised learning. In supervised learning we infer a function from labeled training data. The goal of supervised learning algorithms is learning a good hypothesis that minimizes the sum of the errors. A wide range of supervised algorithms is available such as decision tress, SVM, and KNN methods. In this paper we focus on decision tree algorithms. When we use the decision tree algorithms, the data is partitioned by axis- aligned hyper planes. The geometric concept of decision tree algorithms is relative to separability problems in computational geometry. One of the famous problems in separability concept is computing the maximum bichromatic discrepancy problem. There exists an -time algorithm to compute the maximum bichromatic discrepancy in d dimensions. This problem is closely relative to decision trees in machine learning. We implement this problem in 1, 2, 3 and d dimension. Also, we implement the C4.5 algorithm. The experiments showed that results of this algorithm and C4.5 algorithm are comparable.