Using directional curvatures to visualize folding patterns of the GTM projection manifolds

Peter Tino, Ian T. Nabney, Yi Sun

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

Abstract

In data visualization, characterizing local geometric properties of non-linear projection manifolds provides the user with valuable additional information that can influence further steps in the data analysis. We take advantage of the smooth character of GTM projection manifold and analytically calculate its local directional curvatures. Curvature plots are useful for detecting regions where geometry is distorted, for changing the amount of regularization in non-linear projection manifolds, and for choosing regions of interest when constructing detailed lower-level visualization plots.
Original languageEnglish
Title of host publicationArtificial Neural Networks — ICANN 2001
EditorsG. Dorffner, H. Bischof, K. Hornik.
PublisherSpringer
Pages421-428
Number of pages8
Volume2130
ISBN (Print)3540424865, 9783540446682
DOIs
Publication statusPublished - 1 Jan 2001
EventInternational Conference on Artificial Neural Networks, ICANN 2001 - Vienna, Austria
Duration: 21 Aug 200125 Aug 2001

Publication series

NameLecture Notes in Computer Science
PublisherSpringer-Verlag

Conference

ConferenceInternational Conference on Artificial Neural Networks, ICANN 2001
CountryAustria
CityVienna
Period21/08/0125/08/01

Fingerprint

Data visualization
Visualization
Geometry

Bibliographical note

The original publication is available at www.springerlink.com

Keywords

  • data visualization
  • non-linear projection manifolds
  • directional curvatures
  • curvature plots
  • geometry
  • visualization plots

Cite this

Tino, P., Nabney, I. T., & Sun, Y. (2001). Using directional curvatures to visualize folding patterns of the GTM projection manifolds. In G. Dorffner, H. Bischof, & K. Hornik. (Eds.), Artificial Neural Networks — ICANN 2001 (Vol. 2130, pp. 421-428). (Lecture Notes in Computer Science). Springer. https://doi.org/10.1007/3-540-44668-0_59
Tino, Peter ; Nabney, Ian T. ; Sun, Yi. / Using directional curvatures to visualize folding patterns of the GTM projection manifolds. Artificial Neural Networks — ICANN 2001. editor / G. Dorffner ; H. Bischof ; K. Hornik. Vol. 2130 Springer, 2001. pp. 421-428 (Lecture Notes in Computer Science).
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Tino, P, Nabney, IT & Sun, Y 2001, Using directional curvatures to visualize folding patterns of the GTM projection manifolds. in G Dorffner, H Bischof & K Hornik. (eds), Artificial Neural Networks — ICANN 2001. vol. 2130, Lecture Notes in Computer Science, Springer, pp. 421-428, International Conference on Artificial Neural Networks, ICANN 2001, Vienna, Austria, 21/08/01. https://doi.org/10.1007/3-540-44668-0_59

Using directional curvatures to visualize folding patterns of the GTM projection manifolds. / Tino, Peter; Nabney, Ian T.; Sun, Yi.

Artificial Neural Networks — ICANN 2001. ed. / G. Dorffner; H. Bischof; K. Hornik. Vol. 2130 Springer, 2001. p. 421-428 (Lecture Notes in Computer Science).

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

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Tino P, Nabney IT, Sun Y. Using directional curvatures to visualize folding patterns of the GTM projection manifolds. In Dorffner G, Bischof H, Hornik. K, editors, Artificial Neural Networks — ICANN 2001. Vol. 2130. Springer. 2001. p. 421-428. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-44668-0_59