Kohonen Self-Organizing Map with quantized weights

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

Kohonen Maps

1999, Pages 145–156

Cover image Kohonen Self-Organizing Map with quantized weights

P. Thirana,

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doi:10.1016/B978-044450270-4/50011-5 Get rights and content

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.