Simplified Calculation of Principal Components | Psychometrika | Cambridge Core (original) (raw)

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.

References

Bocher, Maxime, Introduction to Higher Algebra. New York: Macmillan. 1907, xi–xi.Google Scholar

Hotelling, Harold, Analysis of a Complex of Statistical Variables into Principal Components. J. Educ. Psychol., 1933, 24, 417–441.CrossRefGoogle Scholar

Hotelling, Harold, The Most Predictable Criterion. J. Educ. Psychol., 1935, 26, 139–142.CrossRefGoogle Scholar

Kelley, Truman L. Crossroads in the Mind of Man. Stanford University: Stanford University Press, 1928. pp. 238. p. 100.Google Scholar

Kelley, Truman, L.Essential Traits of Mental Life. Cambridge: Harvard University Press. 1935, 145–145.Google Scholar

Whittaker, E. T. and Robinson, G.The Calculus of Observations. London and Glasgow: Blackie & Son, Limited. 1924, xvi–xvi.Google Scholar