Artefactual Structure from Least-Squares Multidimensional Scaling

We consider the problem of illusory or artefactual structure from the visualisation ofhigh-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SSTRESS measure) gives rise to an annular structure when the input data is drawn from a highdimensional isotropicdistribution, and we provide a theoretical justification for this observation.