Data Discretization Unification

Data discretization is defined as a process of converting continuous data attribute values into a finite set of intervals with minimal loss of information. In this paper, we prove that discretization methods based on informational theoretical complexity and the methods based on statistical measures of data dependency are asymptotically equivalent. Furthermore, we define a notion of generalized entropy and prove that discretization methods based on MDLP, Gini Index, AIC, BIC, and Pearson´s X² and G² statistics are all derivable from the generalized entropy function. We design a dynamic programming algorithm that guarantees the best discretization based on the generalized entropy notion. Furthermore, we conducted an extensive performance evaluation of our method for several publicly available data sets. Our results show that our method delivers on the average 31% less classification errors than many previously known discretization methods.