Using Directional Curvatures to Visualize Folding Patterns of the GTM Projection Manifolds

Authors:
Peter Tino;Ian Nabney;Yi Sun
Affiliations:
-;-;-
Venue:
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Year:
2001

Citing 3
Cited 1

Matrix analysis

Matrix analysis
GTM: the generative topographic mapping

Neural Computation
Neural Networks for Pattern Recognition

Neural Networks for Pattern Recognition

Guiding local regression using visualisation

Proceedings of the First international conference on Deterministic and Statistical Methods in Machine Learning

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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.