Affiliations: Artificial Intelligence Research Institute (IIIA), Spanish Council for Scientific Research (CSIC), Campus UAB, 08193 Bellaterra, Spain E‐mail: {mantaras,cerquide,pere}@iiia.csic.es
Abstract: In [7], a new information‐theoretic attribute selection method for decision tree induction was introduced. This method consists in computing for each node, a distance between the partition generated by the values of each candidate attribute in the node and the correct partition of the subset of training examples in this node. The chosen attribute is that whose corresponding partition is the closest to the correct partition (i.e., the partition that perfectly classifies the training data). In that paper it was also formally proved that such distance is not biased towards attributes with a large number of values in the sense specified by Quinlan in [12] and some initial experimental evidence suggests that the predictive accuracy of the induced trees was not significantly different from that obtained with the most widely used information theoretic attribute selection measures, that is, Quinlan’s Gain and Quinlan’s Gain Ratio. However, it seemed that the distance induced smaller trees especially when the attributes had different number of values. In that paper it was not confirmed that the differences were statistically significant due to the small number of experiments performed. In this paper we report experimental results that allow to confirm that the distance induces trees whose size, without losing accuracy, is not significantly different from those obtained using Quinlan’s Gain but smaller than those obtained with Quinlan’s Gain Ratio. These experimental results are supported by a statistical analysis performed using two statistical hypothesis tests: the sign test and the signed rank test.
