Discretization of continuous features

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]

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

See also

• Density estimation
• Continuity correction

References

1. Clarke, E. J.; Barton, B. A. (2000). "Entropy and MDL discretization of continuous variables for Bayesian belief networks" (PDF). International Journal of Intelligent Systems. 15: 61–92. doi:10.1002/(SICI)1098-111X(200001)15:1<61::AID-INT4>3.0.CO;2-O. Retrieved 2008-07-10.
2. Fayyad, Usama M.; Irani, Keki B. (1993) "Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning" (PDF). 29 July 2023. hdl:2014/35171., Proc. 13th Int. Joint Conf. on Artificial Intelligence (Q334 .I571 1993), pp. 1022-1027
3. Dougherty, J.; Kohavi, R.; Sahami, M. (1995). "Supervised and Unsupervised Discretization of Continuous Features". In A. Prieditis & S. J. Russell, eds. Work. Morgan Kaufmann, pp. 194-202
4. Kotsiantis, S.; Kanellopoulos, D (2006). "Discretization Techniques: A recent survey". GESTS International Transactions on Computer Science and Engineering. 32 (1): 47–58. CiteSeerX 10.1.1.109.3084.