Matching the dimensionality of maps with that of the data

Authors:
Colin Fyfe
Affiliations:
Applied Computational Intelligence Research Unit, The University of Paisley, Paisley, Scotland
Venue:
SMO'05 Proceedings of the 5th WSEAS international conference on Simulation, modelling and optimization
Year:
2005

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Abstract

Topographic maps are low dimensional maps which retain some topology of the original dataset. Many topographic mappings suffer from having the dimensionality of the map determined beforehand which is certain to be inappropriate for some data sets. In this paper, we develop a method of investigating a data set enabling the local dimensionality of the map to change. Our model of the data allows us to traverse the main manifold on which the data lies while giving information about the local dimensionality of the data around this main manifold.