DOI: 10.1007/bf00201801. Self-organizing maps: ordering, convergence properties and energy functions

Self-organizing maps: ordering, convergence properties and energy functions

10.1007/bf00201801

Crossref journal-article

Springer Science and Business Media LLC

Biological Cybernetics (297)

Bibliography

Erwin, E., Obermayer, K., & Schulten, K. (1992). Self-organizing maps: ordering, convergence properties and energy functions. Biological Cybernetics, 67(1), 47â55.

Authors 3

E. Erwin (first)
K. Obermayer (additional)
K. Schulten (additional)

References 28 Referenced 281

Cottrell M, Fort JC (1987) Etude d'un processus d'auto-organization. Ann Inst Henri Poincaré 23:1–20 / Ann Inst Henri Poincaré by M Cottrell (1987)
Durbin R, Mitchison G (1990) A dimension reduction framework for understanding cortical maps. Nature 343:644–647 (10.1038/343644a0) / Nature by R Durbin (1990)
Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689–691 (10.1038/326689a0) / Nature by R Durbin (1987)
Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: Stationary states, metastability and convergence rate. Biol Cybern (this issue) (10.1007/BF00201800)
Favata F, Walker R (1991) A study of the application of Kohonentype neural networks to the travelling salesman problem. Biol Cybern 64:463–468 (10.1007/BF00202610) / Biol Cybern by F Favata (1991)
Geszti T (1990) Physical models of neural networks. World Scientific, Singapore (10.1142/0925) / Physical models of neural networks by T Geszti (1990)
Hertz J, Krogh A, Palmer RG (1991) Introduction to the theory of neural computation. Addison-Wesley, Redwood City, California / Introduction to the theory of neural computation by J Hertz (1991)
Kohonen T (1982a) Analysis of a simple self-organizing process. Biol Cybern 44:135–140 (10.1007/BF00317973) / Biol Cybern by T Kohonen (1982)
Kohonen T (1982b) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69 (10.1007/BF00337288) / Biol Cybern by T Kohonen (1982)
Kohonen T (1988) Self-organization and associative memory. Springer, New York Berlin Heidelberg (10.1007/978-3-662-00784-6) / Self-organization and associative memory by T Kohonen (1988)
Kohonen T (1989) Speech recognition based on topology preserving neural maps. In: Aleksander I (ed) Neural computation. London, Kogan Page / Neural computation by T Kohonen (1989)
Kohonen T (1991) Self-organizing maps: optimization approaches. In: Kohonen T et al. (ed) Artificial neural networks, vol II. North Holland, Amsterdam, pp 981–990 (10.1016/B978-0-444-89178-5.50003-8) / Artificial neural networks, vol II by T Kohonen (1991)
Lo ZP, Bavarian B (1991) On the rate of convergence in topology preserving neural networks. Biol Cybern 65:55–63 (10.1007/BF00197290) / Biol Cybern by ZP Lo (1991)
Luttrell SP (1989) Self-organization: a derivation from first principles of a class of learning algorithms. In: Proc. 3rd IEEE Int. Joint Conf. on Neural Networks, vol II. Washington, pp 495–498, IEEE Neural Networks Council (10.1109/IJCNN.1989.118288) / Proc. 3rd IEEE Int. Joint Conf. on Neural Networks, vol II. by SP Luttrell (1989)
Moon P, Spencer DE (1969) Partial differential equations. Heath, Lexington, Mass / Partial differential equations by P Moon (1969)
Obermayer K, Ritter H, Schulten K (1990a) Large-scale simulations of self-organizing neural networks on parallel computers: Applications to biological modelling. Parallel Computer 14: 381–404 (10.1016/0167-8191(90)90088-Q) / Parallel Computer by K Obermayer (1990)
Obermayer K, Ritter H, Schulten K (1990b) A principle for the formation of the spatial structure of cortical feature maps. Proc Natl Acad Sci USA 87:8345–8349 (10.1073/pnas.87.21.8345) / Proc Natl Acad Sci USA by K Obermayer (1990)
Obermayer K, Blasdel GG, Schulten K (1991) A neural network model for the formation of the spatial structure of retinotopic maps, orientationand ocular dominance columns. In: Kohonen T et al. (ed) Artificial neural networks, vol I. North Holland, Amsterdam, pp 505–511 / Artificial neural networks, vol I by K Obermayer (1991)
Ritter H (1988) Selbstorganisierende neuronale Karten. PhD thesis. Technische Universität München
Ritter H, Kohonen T (1989) Self-organizing semantic maps. Biol Cybern 61:241–254 (10.1007/BF00203171) / Biol Cybern by H Ritter (1989)
Ritter H, Schulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping. Biol Cybern 54:99–106 (10.1007/BF00320480) / Biol Cybern by H Ritter (1986)
Ritter H, Schulten K (1988) Convergence properties of Kohonen's topology conserving mappings: Fluctuatuions, stability and dimension selection. Biol Cybern 60:59–71 (10.1007/BF00205972) / Biol Cybern by H Ritter (1988)
Ritter H, Martinetz T, Schulten K (1989) Topology conserving maps for learning visuomotor-coordination. Neural Networks 2:159–168 (10.1016/0893-6080(89)90001-4) / Neural Networks by H Ritter (1989)
Robbins H, Munro S (1951) A stochastic approximation method. Ann Math Statist 22:400–407 (10.1214/aoms/1177729586) / Ann Math Statist by H Robbins (1951)
Schottes JC (1991) Unsupervised context learning in natural language processing. In: Proc 5th IEEE Int. Joint Conf. on Neural Networks, vol I. Washington, pp 107–112, IEEE Neural Networks Council / Proc 5th IEEE Int. Joint Conf. on Neural Networks, vol I. by JC Schottes (1991)
Simic PD (1989) Statistical mechanics as the underlying theory of ‘elastic’ and ‘neural’ optimizations. Network 1:89–103 (10.1088/0954-898X_1_1_007) / Network by PD Simic (1989)
Tolat VV (1990) An analysis of Kohonen's self-organizing maps using a system of energy functions. Biol Cybern 64:155–164 (10.1007/BF02331345) / Biol Cybern by VV Tolat (1990)
van Kämpen NG (1981) Stochastic process in physics and chemistry. North-Holland, Amsterdam / Stochastic process in physics and chemistry by NG Kämpen van (1981)

Dates

Type	When
Created	21 years ago (Aug. 30, 2004, 1:54 p.m.)
Deposited	6 years, 4 months ago (April 3, 2019, 6:27 a.m.)
Indexed	3 weeks, 3 days ago (Aug. 7, 2025, 5:05 p.m.)
Issued	33 years, 4 months ago (May 1, 1992)
Published	33 years, 4 months ago (May 1, 1992)
Published Print	33 years, 4 months ago (May 1, 1992)

Funders 0

None

BibTeX

@article{Erwin_1992, title={Self-organizing maps: ordering, convergence properties and energy functions}, volume={67}, ISSN={1432-0770}, url={http://dx.doi.org/10.1007/bf00201801}, DOI={10.1007/bf00201801}, number={1}, journal={Biological Cybernetics}, publisher={Springer Science and Business Media LLC}, author={Erwin, E. and Obermayer, K. and Schulten, K.}, year={1992}, month=may, pages={47–55} }

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