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In many classification models, data is discretized to better estimate itsdistribution. Existing discretization methods often target at maximizing thediscriminant power of discretized data, while overlooking the fact that theprimary target of data discretization in classification is to improve thegeneralization performance. As a result, the data tend to be over-split intomany small bins since the data without discretization retain the maximaldiscriminant information. Thus, we propose a Max-Dependency-Min-Divergence(MDmD) criterion that maximizes both the discriminant information andgeneralization ability of the discretized data. More specifically, theMax-Dependency criterion maximizes the statistical dependency between thediscretized data and the classification variable while the Min-Divergencecriterion explicitly minimizes the JS-divergence between the training data andthe validation data for a given discretization scheme. The proposed MDmDcriterion is technically appealing, but it is difficult to reliably estimatethe high-order joint distributions of attributes and the classificationvariable. We hence further propose a more practical solution,Max-Relevance-Min-Divergence (MRmD) discretization scheme, where each attributeis discretized separately, by simultaneously maximizing the discriminantinformation and the generalization ability of the discretized data. Theproposed MRmD is compared with the state-of-the-art discretization algorithmsunder the naive Bayes classification framework on 45 machine-learning benchmarkdatasets. It significantly outperforms all the compared methods on most of thedatasets.

A Max-relevance-min-divergence Criterion for Data Discretization with Applications on Naive Bayes