Title :
On the existence and stability of solutions in self-organizing cortical maps
Author :
Meyer-Bäse, Anke
Author_Institution :
Dept. of Comput. & Electr. Eng., Florida Univ., Gainesville, FL, USA
Abstract :
Based on the mathematical formulation by Amaris (1982, 1983) of the self-organization of synaptic efficacies and neural response fields under the influence of external stimuli, the authors show that if a map is a contraction then the system has a unique equilibrium which is globally asymptotically stable and can be approximated closely by iterations; consequently the system acts as a stable encoder of external input stimuli. The system converges to a fixed point representing the steady-state of the neural activity and describes a superposition of the spatial integrals of the weight function between neighbouring neurons and the stimulus autocorrelation function
Keywords :
asymptotic stability; brain models; correlation theory; encoding; neurophysiology; self-organising feature maps; fixed point convergence; global asymptotic stability; iterations; neural activity steady state; neural nets; neural response fields; self-organizing cortical maps; spatial integrals; stability; stable encoder; stimulus autocorrelation function; synaptic efficacies; weight function; Autocorrelation; Extraterrestrial measurements; Integral equations; Kernel; Neurons; Nonlinear equations; Probability distribution; Stability; Steady-state;
Conference_Titel :
Neural Networks Proceedings, 1998. IEEE World Congress on Computational Intelligence. The 1998 IEEE International Joint Conference on
Conference_Location :
Anchorage, AK
Print_ISBN :
0-7803-4859-1
DOI :
10.1109/IJCNN.1998.686001
