SOM's mathematics

Neural Networks

Volumn 19, Issue 6-7, 2006, Pages 812-816

  Fort, J C ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Grid equilibrium; Limit theorems; Magnification factor; Topology preservation

Indexed keywords

NUMERICAL ANALYSIS; TOPOLOGY;

GRID EQUILIBRIUM; LIMIT THEOREMS; MAGNIFICATION FACTOR; TOPOLOGY PRESERVATION;

THEOREM PROVING;

ALGORITHM; ARTICLE; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICS; PRIORITY JOURNAL; THEORETICAL STUDY;

FRACTALS; MATHEMATICS; MODELS, THEORETICAL;

EID: 33746622513     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2006.05.025     Document Type: Article

References (14)

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4. Delattre S., Fort J.C., and Pagès G. Local distortion and μ-mass of the cells of one dimensional asymptotically optimal quantizers. Communications in Statistics. Theory and Methods 33 5 (2004) 1087-1117
5. Fort J.C., and Pagès G. On the a.s. convergence of the Kohonen algorithm with a general neighborhood function. The Annals of Applied Probability 5 4 (1995) 1177-1216
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10. Pollard D. A central limit theorem for k-means clustering. The Annals of Probability 10 4 (1982) 919-926
11. Ritter H. Asymptotic level for a class of vector quantization process. IEEE Transactions on Neural Networks 2 1 (1991) 173-175
12. Ritter H., and Schulten K. On the stationary state of Kohonen's self-organizing sensory map. Biological Cybernetics 60 1 (1988) 59-71
13. Sadeghi A. Convergence in distribution of the multi-dimensional Kohonen algorithm. Journal of Applied Probability 38 1 (2001) 136-151
14. Villmann T., Der R., Herrmann M., and Martinetz T. Topology preservation in self-organizing feature maps: exact definition and measurement. IEEE Transactions on Neural Networks 8 2 (1997) 256-266