𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Study of the Kohonen network with a discrete state space

✍ Scribed by Patrick Thiran; Martin Hasler

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
462 KB
Volume
38
Category
Article
ISSN
0378-4754

No coin nor oath required. For personal study only.

✦ Synopsis

Digital (or mixed mode) circuit implementations of neural networks bring one major modification to their ideal, defectless models: quantization of the weights dynamics. Would this modification completely perturb the behavior of the network, it will never be possible to implement it on a digital (or mixed mode) VLSI chip. Clearly, the analysis of quantization effects is crucial for practical applications. It has been mainly studied for Hopfield networks and multi-layer networks.

We study this issue in the Kohonen network, since it has received little attention so far. A Kohonen net is a self-organising map preserving the topology of the input space (Kohonen, 1989). The first part of the paper is devoted to the mathematical treatment of the self-organisation property of a one-dimensional array with discrete weights. This property has been already established for continuous-valued weights, we will see that we need additional hypothesis to ensure a correct result when the weights are discrete-valued. The second part presents a qualitative extension of this analysis to more general cases.

πŸ“œ SIMILAR VOLUMES

Polypeptide folding on a conformational-
Polypeptide folding on a conformational-space network: Dependence of network topology on the structural discretization procedure
✍ Roman Affentranger; Xavier Daura πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 494 KB

## Abstract Mapping the conformational space of a polypeptide onto a network of conformational states involves a number of subjective choices, mostly in relation to the definition of conformation and its discrete nature in a network framework. Here, we evaluate the robustness of the topology of con

On the existence of solutions to linear
On the existence of solutions to linear active networks: A state-space approach
✍ M. Chandrashekar; H. K. Kesavan πŸ“‚ Article πŸ“… 1974 πŸ› John Wiley and Sons 🌐 English βš– 542 KB

## Abstract In recent literature, several alternative conditions for the existence of solutions to active networks are given. In this paper, yet another condition is given which is both necessary and sufficient for the existence of a unique solution to the network. Based on this new condition a pre

A Discrete, Space Variation Model for St
A Discrete, Space Variation Model for Studying the Kinetics of Shape Deformation of Vesicles Coupled with Phase Separation
✍ Jianfeng Li; Hongdong Zhang; Ping Tang; Feng Qiu; Yuliang Yang πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 171 KB

## Abstract **Summary:** The evolution dynamics of phase separation, coupled with shape deformation of vesicles is described by using dissipative dynamic equations, specifically the time‐dependent Ginzburg‐Landau (TDGL) equations. In order to improve the numerical stability and thus to efficiently