In statistics and machine learning, discretization refers to the process of converting or partitioning continuous attributes, features or variables to discretized or nominal attributes/features/variables/intervals. This can be useful when creating probability mass functions – formally, in density estimation. It is a form of discretization in general and also of binning, as in making a histogram. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level considered negligible for the modeling purposes at hand.

Typically data is discretized into partitions of K equal lengths/width (equal intervals) or K% of the total data (equal frequencies).^[1]

Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method,^[2] which uses mutual information to recursively define the best bins, CAIM, CACC, Ameva, and many others^[3]

Many machine learning algorithms are known to produce better models by discretizing continuous attributes.^[4]

This is a partial list of software that implement MDL algorithm.

• discretize4crf tool designed to work with popular CRF implementations (C++)
• mdlp in the R package discretization
• Discretize in the R package RWeka

• Density estimation
• Continuity correction