The community problem for Stieltjes matrices

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Abstract

The communality problem in factor analysis is that of reducing the diagonal elements of a correlation matrix so that the resulting matrix will be positive semidefinite and of minimum rank. The problem is well studied, but no effective solution procedures have been devised. In this paper, we propose a variant problem and give an algorithm for its solution. We prove that a solution to this problem also solves the communality problem if the correlation matrix is Stieltjes.

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Research supported in part by U.S. Army Research Office Grant DAAG 29-78-G0179 and by National Science Foundation Grant MCS78-17697 while the author was a visitor at Stanford University.