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
γ-Observable neighbours for vector quantization
Neural Networks - New developments in self-organizing maps
A 'Recruiting Neural-Gas' for Function Approximation
IJCNN '00 Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks (IJCNN'00)-Volume 3 - Volume 3
IEEE Transactions on Information Theory
`Neural-gas' network for vector quantization and its application to time-series prediction
IEEE Transactions on Neural Networks
A sequential algorithm for training the SOM prototypes based on higher-order recursive equations
Advances in Artificial Neural Systems
| Hi-index | 0.00 |
The adaptation rule of Vector Quantization algorithms, and consequently the convergence of the generated sequence, depends on the existence and properties of a function called the energy function, defined on a topological manifold. Our aim is to investigate the conditions of existence of such a function for a class of algorithms including the well-known 'K-means' and 'Self-Organizing Map' algorithms. The results presented here extend several previous studies and show that the energy function is not always a potential but at least the uniform limit of a series of potential functions which we call a pseudo-potential. It also shows that a large number of existing vector quantization algorithms developed by the Artificial Neural Networks community fall into this class. The framework we define opens the way to studying the convergence of all the corresponding adaptation rules at once, and a theorem gives promising insights in that direction.