Discretization is a popular approach to handling numeric attributes in machine learning. We argue that the requirements for effective discretization differ between naive-Bayes learning and many other learning algorithms. We evaluate the effectiveness with naive-Bayes classifiers of nine discretization methods, equal width discretization (EWD), equal frequency discretization (EFD), fuzzy discretization (FD), entropy minimization discretization (EMD), iterative discretization (ID), proportional k-interval discretization (PKID), lazy discretization (LD), nondisjoint discretization (NDD) and weighted proportional k-interval discretization (WPKID). It is found that in general naive-Bayes classifiers trained on data preprocessed by LD, NDD or WPKID achieve lower classification error than those trained on data preprocessed by the other discretization methods. But LD can not scale to large data. This study leads to a new discretization method, weighted non-disjoint discretization (WNDD) that combines WPKID and NDD's advantages. Our experiments show that among all the rival discretization methods, WNDD best helps naive-Bayes classifiers reduce average classification error.

Abstract. The use of different discretization techniques can be expected to affect the classification bias and variance of naive-Bayes classifiers. We call such an effect discretization bias and variance. Proportional kinterval discretization (PKID) tunes discretization bias and variance by adjusting discretized interval size and number proportional to the number of training instances. Theoretical analysis suggests that this is desirable for naive-Bayes classifiers. However PKID is sub-optimal when learning from training data of small size. We argue that this is because PKID equally weighs bias reduction and variance reduction. But for small data, variance reduction can contribute more to lower learning error and thus should be given greater weight than bias reduction. Accordingly we propose weighted proportional k-interval discretization (WPKID), which establishes a more suitable bias and variance trade-off for small data while allowing additional training data to be used to reduce both bias and variance. Our experiments demonstrate that for naive-Bayes classifiers, WPKID improves upon PKID for smaller datasets 1 with significant frequency; and WPKID delivers lower classification error significantly more often than not in comparison to three other leading alternative discretization techniques studied. 1