Artefactual structure from least squares multidimensional scaling

Nicholas P. Hughes, David Lowe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of illusory or artefactual structure from the visualisation of high-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 high-dimensional isotropic distribution, and we provide a theoretical justification for this observation.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems
EditorsS. Becker, S. Thrun, K. Obermeyer
Number of pages8
Publication statusPublished - 2003
Event16th Annual Neural Information Processing Systems Conference, NIPS 2002 - Vancouver, BC, United Kingdom
Duration: 9 Dec 200214 Dec 2002

Conference

Conference16th Annual Neural Information Processing Systems Conference, NIPS 2002
CountryUnited Kingdom
CityVancouver, BC
Period9/12/0214/12/02

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Keywords

  • Problem of illusory
  • artefactual structure
  • visualisation
  • high-dimensional structureless data
  • topographic mappings
  • squared Euclidean metric
  • high-dimensional isotropic distribution

Cite this

Hughes, N. P., & Lowe, D. (2003). Artefactual structure from least squares multidimensional scaling. In S. Becker, S. Thrun, & K. Obermeyer (Eds.), Advances in Neural Information Processing Systems
Hughes, Nicholas P. ; Lowe, David. / Artefactual structure from least squares multidimensional scaling. Advances in Neural Information Processing Systems. editor / S. Becker ; S. Thrun ; K. Obermeyer. 2003.
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Hughes, NP & Lowe, D 2003, Artefactual structure from least squares multidimensional scaling. in S Becker, S Thrun & K Obermeyer (eds), Advances in Neural Information Processing Systems. 16th Annual Neural Information Processing Systems Conference, NIPS 2002, Vancouver, BC, United Kingdom, 9/12/02.

Artefactual structure from least squares multidimensional scaling. / Hughes, Nicholas P.; Lowe, David.

Advances in Neural Information Processing Systems. ed. / S. Becker; S. Thrun; K. Obermeyer. 2003.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - We consider the problem of illusory or artefactual structure from the visualisation of high-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 high-dimensional isotropic distribution, and we provide a theoretical justification for this observation.

AB - We consider the problem of illusory or artefactual structure from the visualisation of high-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 high-dimensional isotropic distribution, and we provide a theoretical justification for this observation.

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Hughes NP, Lowe D. Artefactual structure from least squares multidimensional scaling. In Becker S, Thrun S, Obermeyer K, editors, Advances in Neural Information Processing Systems. 2003