Global Minima by Penalized Full-dimensional Scaling

TL;DR

This paper introduces a method combining full-dimensional MDS with a quadratic penalty to approximate global minima, demonstrated through low-dimensional examples.

Contribution

It proposes a novel approach using penalized stress minimization trajectories to find global minima in multidimensional scaling.

Findings

Effective in low-dimensional examples

Provides a new heuristic for global minima

Demonstrates potential for complex MDS problems

Abstract

The full-dimensional (metric, Euclidean, least squares) multidimensional scaling stress loss function is combined with a quadratic external penalty function term. The trajectory of minimizers of stress for increasing values of the penalty parameter is then used to find (tentative) global minima for low-dimensional multidimensional scaling. This is illustrated with several one-dimensional and two-dimensional examples.