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Classification by Multivariate Analysis

Published online by Cambridge University Press:  01 January 2025

T. W. Anderson
T. W. Anderson*
Affiliation:
Columbia University
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Abstract

The problem considered is the use of a set of measurements on an individual to decide from which of several populations he has been drawn. It is assumed that in each population there is a probability distribution of the measurements. Principles for choosing the rule of classification are based on costs of misclassification. Optimum procedures are derived in general terms. If the measurements are normally distributed, the procedures use one discriminant function in the case of two populations and several discriminant functions in the cases of more populations. The numerical example given involves three normal populations.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 1 , March 1951 , pp. 31 - 50
Copyright
Copyright © 1951 The Psychometric Society

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Footnotes

*

Sponsored in part by the Office of Naval Research.

†

The general theory described in this paper can be deduced as a special case of A. Wald's theory (9). M. A. Girshick presented some of this theory to the meeting of the Institute of Mathematical Statistics at Berkeley, June 16, 1949, in “Bayes, Minimax and Other Approaches to Multiple Classification Problems,” and G. W. Brown (2) described some of the results before the American Statistical Asaociation at Cleveland, December 27, 1948.

References

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