The out-of-sample problem for classical multidimensional scaling

Authors:
Michael W. Trosset;Carey E. Priebe
Affiliations:
Department of Statistics, Indiana University, Bloomington, IN 47405, USA;Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

Out-of-sample embedding techniques insert additional points into previously constructed configurations. An out-of-sample extension of classical multidimensional scaling is presented. The out-of-sample extension is formulated as an unconstrained nonlinear least-squares problem. The objective function is a fourth-order polynomial, easily minimized by standard gradient-based methods for numerical optimization. Two examples are presented.