Artefactual Structure from Least-Squares Multidimensional Scaling

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Nicholas Hughes, David Lowe


We consider the problem of illusory or artefactual structure from the vi- sualisation of high-dimensional structureless data. In particular we ex- amine 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 SS TRESS measure) gives rise to an annular structure when the input data is drawn from a high- dimensional isotropic distribution, and we provide a theoretical justifica- tion for this observation.