Embedding in space forms

David A. Johannsen and Jeffrey L. Solka

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 171-188

Abstract: The goal of this paper is to give explicit procedures and equations for performing metric multidimensional scaling to surfaces. More specifically, we describe a method for determining a configuration of points in a closed and orientable surface (i.e., the MDS space) for which the interpoint distances closely approximate a given set of dissimilarities. More generally, these constant sectional curvature surfaces are examples of space forms (spaces which are quotients of Euclidean, spherical, or hyperbolic space by a subgroup of the isometry group of the space). We will cast our work in this language, thereby allowing the theory to easily be generalized to higher dimensions.

Keywords: Metric MDS; Space form; Surface; Steepest descent minimization (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.jmva.2012.06.002

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