Analysing a self-organising algorithm

Neural Networks

Volumn 10, Issue 5, 1997, Pages 875-883

  Flanagan, John A ^a,b  

^a SWISS FEDERAL INSTITUTE OF TECHNOLOGY   (Switzerland)

^b EPFL   (Switzerland)

Author keywords

Connectedness; Ordinary differential equation method; Self organisation

Indexed keywords

ALGORITHM; ARTIFICIAL NEURAL NETWORK; PRIORITY JOURNAL; SHORT SURVEY;

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

SELF ORGANIZING ALGORITHM;

NEURAL NETWORKS;

EID: 0030616346     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(96)00114-1     Document Type: Article

References (14)

1. Beneveniste, A., Métivier, M., & Priouret, P. (1990). Adaptive Algorithms and Stochastic Approximation, volume 22 of Applications of mathematics. New York: Springer-Verlag.
2. Bouton, C., & Pagès, G. (1993). Self-organisation of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli. Stochastic Processes and their Applications, 47, 249-274.
3. Cottrell, M., & Fort, J. (1986). A stochastic model of retinotopy: A self organising process. Biological Cybernetics, 53, 405-411.
4. Cottrell, M., & Fort, J. (1987). Étude d'un processus d'auto-organisation. Ann. Inst. Henri Poincaré, 23 (1), 1-20.
5. Cottrell, M., Fort, J., & Pagès, G. (1994). Two or three things we know about the Kohonen algorithm. In European Symposium on Artifical Neural Networks, Brussels. Brussels: Dfacto.
6. Gantmacher, F.R. (1966). Théorie des matrices. Paris: Dunod.
7. Kaplan, W. (1981). Advanced mathematics for engineers. New York: Addison-Wesley.
8. Kohonen, T. (1995). Self-organising maps. New York: Springer-Verlag.
9. Kushner, H.J., & Clark, D.S. (1978). Stochastic approximation methods for constrained and unconstrained systems, applied mathematical sciences. Vol. 26. New York: Springer-Verlag.
10. Ljung, L. (1977). Analysis of recursive stochastic algorithms. IEEE Transactions on Automatic Control, AC-22 (4), 551-575.
11. Ritter, H., Martinez, T., & Schulten, K. (1992). Neural computation and self-organising maps. Reading, MA: Addison-Wesley.
12. Robbins, H., & Monro, S. (1951). A stochastic approximation method. Ann. Math. Stat., 22, 400-407.
13. Thiran, P., & Hasler, M. (1994). Self-organisation of a one dimensional Kohonen network with quantized weights and inputs. Neural Networks, 1 (9), 1427-1439.
14. Yang, H., & Dillon, T.S. (1992). Convergence of self-organising neural algorithms. Neural Networks, 5, 485-493.