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Simplified Calculation of Principal Components

Published online by Cambridge University Press:  01 January 2025

Harold Hotelling
Harold Hotelling*
Affiliation:
Columbia University, New York
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Abstract

The resolution of a set of n tests or other variates into components γn, each of which accounts for the greatest possible portion γ1, γ2, ..., of the total variance of the tests unaccounted for by the previous components, has been dealt with by the author in a previous paper. Such “factors,” on account of their analogy with the principal axes of a quadric, have been called principal components. The present paper describes a modification of the iterative scheme of calculating principal components there presented, in a fashion that materially accelerates convergence. The application of the iterative process is not confined to statistics, but may be used to obtain the magnitudes and orientations of the principal axes of a quadric or hyperquadric in a manner which will ordinarily be far less laborious than those given in books on geometry. This is true whether the quadrics are ellipsoids or hyperboloids; the proof of convergence given in an earlier paper is applicable to all kinds of central quadrics.

Type
Original Paper
Information
Psychometrika , Volume 1 , Issue 1 , March 1936 , pp. 27 - 35
Copyright
Copyright © 1936 The Psychometric Society

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References

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