statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

and

machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...

, 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 applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numeri ...

in general and also of binning, as in making a

histogram A histogram is a visual representation of the frequency distribution, distribution of quantitative data. To construct a histogram, the first step is to Data binning, "bin" (or "bucket") the range of values— divide the entire range of values in ...

. 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). Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method, which uses

mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statistical dependence, dependence between the two variables. More specifically, it quantifies the "Information conten ...

to recursively define the best bins, CAIM, CACC, Ameva, and many others Many machine learning algorithms are known to produce better models by discretizing continuous attributes.

Software

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

References

Estimation of densities Statistical data coding {{statistics-stub

Software

See also

References