Discretization is an essential preprocessing technique used in many knowledge discovery and data mining tasks. Its main goal is to transform a set of continuous attributes into discrete ones, by associating categorical values to intervals and thus transforming quantitative data into qualitative data. In this manner, symbolic data mining algorithms can be applied over continuous data and the representation of information is simplified, making it more concise and specific. The literature provides numerous proposals of discretization and some attempts to categorize them into a taxonomy can be found. However, in previous papers, there is a lack of consensus in the definition of the properties and no formal categorization has been established yet, which may be confusing for practitioners. Furthermore, only a small set of discretizers have been widely considered, while many other methods have gone unnoticed. With the intention of alleviating these problems, this paper provides a survey of discretization methods proposed in the literature from a theoretical and empirical perspective. From the theoretical perspective, we develop a taxonomy based on the main properties pointed out in previous research, unifying the notation and including all the known methods up to date. Empirically, we conduct an experimental study in supervised classification involving the most representative and newest discretizers, different types of classifiers, and a large number of data sets. The results of their performances measured in terms of accuracy, number of intervals, and inconsistency have been verified by means of nonparametric statistical tests. Additionally, a set of discretizers are highlighted as the best performing ones.

Cross-validation is a very commonly employed technique used to evaluate classifier performance. However, it can potentially introduce dataset shift, a harmful factor that is often not taken into account and can result in inaccurate performance estimation. This paper analyzes the prevalence and impact of partition-induced covariate shift on different k -fold cross-validation schemes. From the experimental results obtained, we conclude that the degree of partition-induced covariate shift depends on the cross-validation scheme considered. In this way, worse schemes may harm the correctness of a single-classifier performance estimation and also increase the needed number of repetitions of cross-validation to reach a stable performance estimation.