Encyclopedia of Machine Learning and Data Mining

2017 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Linear Discriminant

  • Novi QuadriantoEmail author
  • Wray L. Buntine
Reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7687-1_480


A discriminant is a function that takes an input variable x and outputs a class label y for it. A linear discriminant is a discriminant that uses a linear function of the input variables and more generally a linear function of some vector function of the input variables f(x).

This entry focuses on one such linear discriminant function called Fisher’s linear discriminant. Fisher’s discriminant works by finding a projection of input variables to a lower dimensional space while maintaining a class separability property.

Motivation and Background

The curse of dimensionality ( Curse of Dimensionality) is an ongoing problem in applying statistical techniques to pattern recognition problems. Techniques that are computationally tractable in low-dimensional spaces can become completely impractical in high-dimensional spaces. Consequently, various methods have been proposed to reduce the dimensionality of the input or feature space in the hope of obtaining a more manageable problem....

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Recommended Reading1

  1. Bellman RE (1961) Adaptive control processes. Princeton University Press, PrincetonzbMATHCrossRefGoogle Scholar
  2. Bishop C (2006) Pattern recognition and machine learning. Springer, New YorkzbMATHGoogle Scholar
  3. Duda RO, Hart PE (1973) Pattern classification and scene analysis. Wiley, New YorkzbMATHGoogle Scholar
  4. Fukunaga K (1990) Introduction to statistical pattern recognition, 2nd edn. Academic, San DiegozbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Informatics, SMiLe CLiNiCUniversity of SussexBrightonUK
  2. 2.Statistical Machine Learning ProgramNICTACanberraAustralia
  3. 3.Faculty of Information TechnologyMonash UniversityClaytonAustralia