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 proceedingChapter in a book

5 Citations (Scopus)
11 Downloads (Pure)


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.
Place of PublicationGermany
Number of pages8
ISBN (Print)3540424865
Publication statusPublished - 1 Jan 2001

Publication series

NameLecture Notes in Computer Science

Bibliographical note

The original publication is available at


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


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