ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

On the Use of Second-Order Information in Distance Geometry and Multidimensional Scaling

Michael Trosset
Department of Mathematics College of William and Mary

Tuesday, June 4, 2002 15:00-16:00,
Room 145, NIST North (820)
Tuesday, June 4, 2002 13:00-14:00,
Room 4550

Abstract: Multidimensional Scaling (MDS) is a collection of techniques for constructing configurations of points from information about interpoint distances. Originally developed for psychometric applications, MDS is now widely used to visualize multivariate data sets. Important contemporary applications include the problem of inferring the 3-dimensional structure of a molecule from information about its interatomic distances. MDS can be formulated as a collection of optimization problems, most of which require numerical solution. Most well-known MDS algorithms are actually first-order (gradient) methods for solving specific optimization problems. Some researchers have argued that second-order methods are inappropriate for MDS. This talk presents the case for second-order methods, arguing that the standard objective functions used to formulate MDS have low curvature near solutions and that second-order information is essential if one hopes to compute accurate solutions. I will describe how the use of second-order information led to new insights about the prevalence of nonglobal minimizers of the raw stress criterion, summarize Sibson's (1979) perturbational analysis of classical MDS, and discuss my own efforts to extend classical MDS from the case of fixed dissimilarities to the case of bound-constrained dissimilarity variables.
Contact: A. J. Kearsley

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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