Nonlinear projection using geodesic distances and the neural gas network

Authors:
Pablo A. Estévez;Andrés M. Chong;Claudio M. Held;Claudio A. Perez
Affiliations:
Dept. Electrical Engineering, University of Chile, Santiago, Chile;Dept. Electrical Engineering, University of Chile, Santiago, Chile;Dept. Electrical Engineering, University of Chile, Santiago, Chile;Dept. Electrical Engineering, University of Chile, Santiago, Chile
Venue:
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
Year:
2006

Citing 7
Cited 5

Topology representing networks

Neural Networks
Self-Organizing Maps

Self-Organizing Maps
Nonlinear Projection with the Isotop Method

ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Online data visualization using the neural gas network

Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Nonlinear dimensionality reduction of data manifolds with essential loops

Neurocomputing
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets

IEEE Transactions on Neural Networks
Interactive visualization and analysis of hierarchical neural projections for data mining

IEEE Transactions on Neural Networks

Proceedings of the 5th Annual International Conference on Mobile and Ubiquitous Systems: Computing, Networking, and Services

5th Annual International Conference on Mobile and Ubiquitous Systems: Computing, Networking, and Services
A robust nonlinear projection method using the neural gas network

IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Visualization of topology representing networks

IDEAL'07 Proceedings of the 8th international conference on Intelligent data engineering and automated learning
Topology representing network map: a new tool for visualization of high-dimensional data

Transactions on computational science I
Online dimensionality reduction using competitive learning and Radial Basis Function network

Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

A nonlinear projection method that uses geodesic distances and the neural gas network is proposed. First, the neural gas algorithm is used to obtain codebook vectors, and a connectivity graph is concurrently created by using competitive Hebbian rule. A procedure is added to tear or break non-contractible cycles in the connectivity graph, in order to project efficiently ‘circular’ manifolds such as cylinder or torus. In the second step, the nonlinear projection is created by applying an adaptation rule for codebook positions in the projection space. The mapping quality obtained with the proposed method outperforms CDA and Isotop, in terms of the trustworthiness, continuity, and topology preservation measures.