Preface
Analyzing and representing multidimensional quantitative and qualitative data: Demographic study of the Rhône valley. The domestic consumption of the Canadian families
Value Maps: Finding Value in Markets that are Expensive
Data Mining and Knowledge Discovery with Emergent Self-Organizing Feature Maps for Multivariate Time Series
From Aggregation Operators to Soft Learning Vector Quantization and Clustering Algorithms
Active Learning in Self-Organizing Maps
Point Prototype Generation and Classifier Design
Self-Organizing Maps on non-euclidean Spaces
Self-Organising Maps for Pattern Recognition
Tree Structured Self-Organizing Maps
Growing self-organizing networks—history, status quo, and perspectives
Kohonen Self-Organizing Map with quantized weights
On the Optimization of Self-Organizing Maps by Genetic Algorithms
Self organization of a massive text document collection
Document Classification with Self-Organizing Maps
Navigation in Databases Using Self-Organising Maps
A SOM-based sensing approach to robotic manipulation tasks
SOM-TSP: An approach to optimize surface component mounting on a printed circuit board
Self-Organising Maps in Computer Aided Design of electronic circuits
Modeling Self-Organization in the Visual Cortex
A Spatio-Temporal Memory Based on SOMs with Activity Diffusion
Advances in modeling cortical maps
Topology Preservation in Self-Organizing Maps
Second-Order Learning in Self-Organizing Maps
Energy functions for self-organizing maps
LVQ and single trial EEG classification
Self-organizing map in categorization of voice qualities
Chemometric analyses with self organising feature maps: A worked example of the analysis of cosmetics using Raman spectroscopy
Self-Organizing Maps for Content-Based Image Database Retrieval
Indexing Audio Documents by using Latent Semantic Analysis and SOM
Self-Organizing map in analysis of large-scale industrial systems
Keyword index

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Kohonen Maps

1999, Pages 145–156

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Kohonen Self-Organizing Map with quantized weights

P. Thirana,

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doi:10.1016/B978-044450270-4/50011-5
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Publisher Summary

The purpose of this chapter is to review the convergence properties of the Kohonen self-organizing map (SOM) when the inputs and the weights are quantized. The motivation behind this work and the impact of the results are both of theoretical and practical nature, and it will not be possible to implement it on a digital very-large-scale integration (VLSI) chip. Most of the chapter is focused on the rigorous analysis in the 1-dim setting, where both the weights and the inputs are scalar. Necessary and sufficient conditions for the ordering of scalar quantized weights are established. These results are compared with the ones obtained when the weights are continuous-valued. Finally, it confirms qualitatively this analysis for the 2-dim case.