Title: The STOPS Framework for Parameter Selection in Multidimensional Scaling

Authors: Thomas Rusch, Patrick Mair, Kurt Hornik 

Affiliation: WU Vienna University of Economics and Business

Abstract:
Multidimensional scaling (MDS) represent objects in a low dimensional
configuration so that fitted distances between objects optimally approximate
multivariate proximities. In recent years MDS has enjoyed a resurgence of
interest mostly by the invention of novel nonlinear MDS models. Those models
employ nonlinear transformations of proximities or distances for representation.
These transformations are governed by parameters. Often it is not clear how the
parameters values should be selected; they are often either chosen ad hoc or
selected by the same mechanism used to fit the MDS model. In this talk we
present a principled way of parameter selection in MDS models based on
structural appearance of the resulting representation. We coin this the STOPS
framework (Structure Optimized Proximity Scaling). In the STOPS framework we
combine a goodness-of-fit measure with information capturing the structural
appearance depending solely on the configuration. We discuss structures of
interest, the type of combination and optimization of the combined loss. We
illustrate the framework with an example from a fMRI study on similarities of
mental states in social cognition.