Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Competitive learning algorithms for vector quantization
Neural Networks
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Topology representing networks
Neural Networks
Computational Geometry: Theory and Applications
Neural Computation and Self-Organizing Maps; An Introduction
Neural Computation and Self-Organizing Maps; An Introduction
On the Use of Self-Organizing Maps for Clustering and Visualization
PKDD '99 Proceedings of the Third European Conference on Principles of Data Mining and Knowledge Discovery
IWANN '97 Proceedings of the International Work-Conference on Artificial and Natural Neural Networks: Biological and Artificial Computation: From Neuroscience to Technology
Area Requirement of Gabriel Drawings
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
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We define the γ-observable neighbourhood and use it in soft-competitive learning for vector quantization. Considering a datum v and a set of n units wi in a Euclidean space, let vi be a point of the segment [vwi] whose position depends on γ a real number between 0 and 1, the γ-observable neighbours (γ-ON) of v are the units wi for which vi is in the Voronoï of wi, i.e. wi is the closest unit to vi. For γ = 1, vi merges with wi, all the units are γ-ON of v, while for γ = 0, vi merges with v, only the closest unit to v is its γ-ON. The size of the neighbourhood decreases from n to 1 while γ goes from 1 to 0. For γ lower or equal to 0.5, the γ-ON of v are also its natural neighbours, i.e. their Voronoï regions share a common boundary with that of v. We show that this neighbourhood used in Vector Quantization gives faster convergence in terms of number of epochs and similar distortion than the Neural-Gas on several benchmark databases, and we propose the fact that it does not have the dimension selection property could explain these results. We show it also presents a new self-organization property we call 'self-distribution'.