Sensitivity analysis of the strain criterion for multidimensional scaling

Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing configurations of points from dissimilarity information about interpoint distances. Classsical MDS assumes a fixed matrix of dissimilarities. However, in some applications, e.g., the problem of inferring 3-dimensional molecular structure from bounds on interatomic distances, the dissimilarities are free to vary, resulting in optimization problems with a spectral objective function. A perturbation analysis is used to compute first- and second-order directional derivatives of this function. The gradient and Hessian are then inferred as representers of the derivatives. This coordinate-free approach reveals the matrix structure of the objective and facilitates writing customized optimization software. Also analyzed is the spectrum of the Hessian of the objective.

• Type: Journal
• Year: 2006
• Where: CSDA
• Authors: R. M. Lewis, M. W. Trosset
• Keywords: CSDA 2006, Data Analytic Techniques, Second-order Directional Derivatives, Spectral Objective Function