An r-Dimensional Quadratic Placement Algorithm

Kenneth M. Hall
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Kenneth M. Hall: Department of General Services, State of California

Management Science, 1970, vol. 17, issue 3, 219-229

Abstract: In this paper the solution to the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given. The criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X'X - 1, for each of the r unknown coordinate vectors. It is proved that the problem reduces to the minimization of a sum or r positive semi-definite quadratic forms which, under the quadratic constraints, reduces to the problem of finding r eigenvectors of a special "disconnection" matrix. It is shown, by example, how this can serve as a basis for cluster identification.

Date: 1970
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:17:y:1970:i:3:p:219-229

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