Abstract
In order to create spatially ordered and organized representations of input occurrences in a neural network, the most essential principle seems to be to confine the learning corrections to subsets of network units that lie in the topological neighborhood of the best-matching unit. There seems to exist an indefinite number of ways to define the matching of an input occurrence with the internal representations, and even the neighborhood of a unit can be defined in many ways. It is neither necessary to define the corrections as gradient steps in the parameter space: improvements in matching may be achieved by batch computation or evolutionary changes. Consequently, all such cases will henceforth be regarded to belong to the broader category of the Self-Organizing Map (SOM) algorithms. This category may also be thought to contain both supervised and unsupervised learning methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling: Numerical Recipes in C — The Art of Scientific Computing (Press Syndicate of the University of Cambridge, Cambridge University Press 1988)
J. Kangas, T. Kohonen, J. Laaksonen, O. Simula, O. Ventä: In Proc. IJCNN’89, Int. Joint Conf. on Neural Networks (IEEE Service Center, Piscataway, NJ 1989) p. II–517
T. Martinetz, K. Schulten: In Proc. Int. Conf. on Artificial Neural Networks (Espoo, Finland), ed. by T. Kohonen, K. Mäkisara, O. Simula, J. Kangas (North-Holland, Amsterdam, Netherlands 1991) p. I–397
T. M. Martinetz, S. G. Berkovich, K. J. Schulten: IEEE Trans, on Neural Networks 4, 558 (1993)
J. Lampinen, E. Oja: In Proc. 6 SCIA, Scand. Conf. on Image Analysis, ed. by M. Pietikäinen, J. Röning (Suomen Hahmontunnistustutkimuksen seura r.y., Helsinki, Finland 1989) p. 120
P. Koikkalainen, E. Oja: In Proc. IJCNN-90, Int. Joint Conf. on Neural Networks (IEEE Service Center, Piscataway, NJ 1990) p. 279
P. Koikkalainen: In Proc. Symp. on Neural Networks in Finland, ed. by A. Bulsari, B. Saxén (Finnish Artificial Intelligence Society, Helsinki, Finland 1993) p. 51
K. K. Truong: In ICASSP’91, Int. Conf. on Acoustics, Speech and Signal Processing (IEEE Service Center, Piscataway, NJ 1991) p. 2789
W. Wan, D. Fraser: In Proc. IJCNN-93-Nagoya, Int. Joint Conf. on Neural Networks (IEEE Service Center, Piscataway, NJ 1993) p. III–2464
W. Wan, D. Fraser: In Proc. of 5th Australian Conf. on Neural Networks, ed. by A. C. Tsoi, T. Downs (University of Queensland, St Lucia, Australia 1994) p. 17
N. M. Allinson, M. T. Brown, M. J. Johnson: In IEE Int. Conf. on Artificial Neural Networks, Publication 313 (IEE, London, UK 1989) p. 261
N. M. Allinson, M. J. Johnson: In New Developments in Neural Computing, ed. by J. G. Taylor, C. L. T. Mannion (Adam-Hilger, Bristol, UK 1989) p. 79
R. Sedgewick: Algorithms (Addison-Wesley, Reading, MA 1983)
J. Kangas: In Proc. IJCNN-90-San Diego, Int. Joint Conf. on Neural Networks (IEEE Comput. Soc. Press, Los Alamitos, CA 1990) p. II–331
J. Kangas: In Artificial Neural Networks, ed. by T. Kohonen, K. Mäkisara, O. Simula, J. Kangas (North-Holland, Amsterdam, Netherlands 1991) p. II–1591
J. Kangas: In Proc. ICASSP’91, Int. Conf. on Acoustics, Speech and Signal Processing (IEEE Service Center, Piscataway, NJ 1991) p. 101
J. Kangas: In Artificial Neural Networks, 2, ed. by I. Aleksander, J. Taylor (North-Holland, Amsterdam, Netherlands 1992) p. I–117
J. Kangas: PhD Thesis (Helsinki University of Technology, Espoo, Finland 1994)
T. Kohonen: Report A42 (Helsinki University of Technology, Laboratory of Computer and Information Science, Espoo, Finalnd 1996)
T. Kohonen, P. Somervuo: In Proc. WSOM’97, Workshop on Self-Organizing Maps (Helsinki University of Technology, Neural Networks Research Centre, Espoo, Finland 1997) p. 2
R. Kaiman, R. Bucy: J. Basic Engr. 83, 95 (1961)
T. Kohonen, K. Mäkisara, T. Saramäki: In Proc. 7ICPR, Int. Conf. on Pattern Recognition (IEEE Computer Soc. Press, Los Alamitos, CA 1984) p. 182
T. Kohonen: Computer 21, 11 (1988)
T. Kohonen: In Computational Intelligence, A Dynamic System Perspective, ed. by M. Palaniswami, Y. Attikiouzel, R. J. Marks II, D. Fogel, T. Fukuda (IEEE Press, New York, NY 1995) p. 17
T. Kohonen: Biol. Cybernetics 75(4) 281 (1996)
T. Kohonen, S. Kaski, H. Lappalainen: Neural Computation 9, 1321 (1997)
J. Daugman: IEEE Trans. Syst., Man, Cybern. 13, 882 (1983)
I. Daubechies: IEEE Trans. Inf. Theory 36, 961 (1990)
J. Daugman: Visual Research 20, 847 (1980)
J. Daugman: J. Opt. Soc. Am. 2, 1160 (1985)
S. Marcelja: J. Opt. Soc. Am. 70, 1297 (1980)
J. Jones, L. Palmer: J. Neurophysiol. 58, 1233 (1987)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kohonen, T. (2001). Variants of SOM. In: Self-Organizing Maps. Springer Series in Information Sciences, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56927-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-56927-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67921-9
Online ISBN: 978-3-642-56927-2
eBook Packages: Springer Book Archive