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The out-of-sample problem for classical multidimensional scaling

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  • Trosset, Michael W.
  • Priebe, Carey E.

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.

Suggested Citation

  • Trosset, Michael W. & Priebe, Carey E., 2008. "The out-of-sample problem for classical multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4635-4642, June.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4635-4642
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    References listed on IDEAS

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    1. Gale Young & A. Householder, 1938. "Discussion of a set of points in terms of their mutual distances," Psychometrika, Springer;The Psychometric Society, vol. 3(1), pages 19-22, March.
    2. Trosset, Michael W. & Priebe, Carey E. & Park, Youngser & Miller, Michael I., 2008. "Semisupervised learning from dissimilarity data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4643-4657, June.
    3. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
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    1. Trosset, Michael W. & Priebe, Carey E. & Park, Youngser & Miller, Michael I., 2008. "Semisupervised learning from dissimilarity data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4643-4657, June.

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