Discriminant Analysis Algorithm

A Discriminant Analysis Algorithm is a classification algorithm that ...

• Context:
  • It can range from being a Linear Discriminant Analysis Algorithm to being a Quadractic Discriminant Analysis Algorithm.
  • …
• Counter-Example(s):
  • a Logistic Regression Algorithm.
• See: Discriminant, Statistical Analysis Task, Multiple Discriminant Analysis, Factor Analysis, Cluster Analysis.

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References

1978

• (Press & Wilson, 1978) ⇒ S. James Press, and Sandra Wilson. (1978). “Choosing Between Logistic Regression and Discriminant Analysis.” In: Journal of the American Statistical Association, 73(364). : http://www.jstor.org/stable/2286261
  • ABSTRACT: Classifying an observation into one of several populations is discriminant analysis, or classification. Relating qualitative variables to other variables through a logistic cdf functional form is logistic regression. Estimators generated for one of these problems are often used in the other. If the populations are normal with identical covariance matrices, discriminant analysis estimators are preferred to logistic regression estimators for the discriminant analysis problem. In most discriminant analysis applications, however, at least one variable is qualitative (ruling out multivariate normality). Under nonnormality, we prefer the logistic regression model with maximum likelihood estimators for solving both problems. In this article we summarize the related arguments, and report on our own supportive empirical studies.
  • QUOTE: … The linear discriminant analysis approach, by contrast, is strictly applicable only when the underlying variables are jointly normal with equal covariance matrices

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