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Discriminant analysis

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Abstract The need for classification arises in most scientific pursuits. Typically, there is interest in ‘classifying’ an entity, say, an individual or object, on the basis of some characteristics (feature variables) measured on the entity. This article focuses on the form of classification known as supervised classification or discriminant analysis. It is applicable in situations where there are data of known origin with respect to the predefined classes from which a classifier can be constructed to assign an unclassified entity to one of these classes. We consider nonparametric and parametric approaches to the construction of classifiers. Consideration is given to recent results on the formation of classifiers in situations where the number of variables p is very large relative to the number of observations n. Methods for estimating the error rates of a classifier are described, including the situation where the classifier has been formed in some optimal way from a relatively small subset of the variables relative to the available number p. In such situations care has to be taken to avoid the selection bias inherent in the ordinarily used error‐rate estimators. WIREs Comput Stat 2012 doi: 10.1002/wics.1219 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

Plot of a mixture density of two univariate normal components in equal proportions with common variance and means and in the cases: (a) ; (b) ; (c) ; (d) .

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Boundaries of Fisher's rule (dotted line) and logistic rule with interaction term (solid line); crosses and circles denote nonleachers and leachers, respectively.

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Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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