Title :
Two theorems for the Kohonen mapping neural network
Author :
Lo, Zhen-Ping ; Yu, Yaoqi ; Bavarian, Behnam
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., Irvine, CA, USA
Abstract :
The authors provide a rigorous treatment of the convergence of the topology preserving neural network which was first proposed by Kohonen. The problem is formulated for a more general case of selecting the neighborhood amplitude of interaction rather than the uniform amplitude. The proof of convergence is based on the well-known Gladyshev theorem which uses Lyapunov´s function method. This proof also provides the relation between the boundary neurons weight vectors and the number of neurons in the network
Keywords :
Lyapunov methods; self-organising feature maps; Gladyshev theorem; Kohonen mapping neural network; Lyapunov´s function method; boundary neurons weight vectors; neighborhood amplitude; proof of convergence; topology preserving neural network; Algorithm design and analysis; Convergence; Equations; Fires; Network topology; Neural networks; Neurons; Random variables; Self-organizing networks; Signal generators;
Conference_Titel :
Neural Networks, 1992. IJCNN., International Joint Conference on
Conference_Location :
Baltimore, MD
Print_ISBN :
0-7803-0559-0
DOI :
10.1109/IJCNN.1992.227227
