Skip to main content

2012 | OriginalPaper | Buchkapitel

Self-organizing Maps

verfasst von : Marc M. Van Hulle

Erschienen in: Handbook of Natural Computing

Verlag: Springer Berlin Heidelberg

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A topographic map is a two-dimensional, nonlinear approximation of a potentially high-dimensional data manifold, which makes it an appealing instrument for visualizing and exploring high-dimensional data. The self-organizing map (SOM) is the most widely used algorithm, and it has led to thousands of applications in very diverse areas. In this chapter we introduce the SOM algorithm, discuss its properties and applications, and also discuss some of its extensions and new types of topographic map formation, such as those that can be used for processing categorical data, time series, and tree-structured data.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Abrantes AJ, Marques JS (1995) Unified approach to snakes, elastic nets, and Kohonen maps. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’95). IEEE Computer Society, Los Alamitos, CA, vol 5, pp 3427–3430 Abrantes AJ, Marques JS (1995) Unified approach to snakes, elastic nets, and Kohonen maps. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’95). IEEE Computer Society, Los Alamitos, CA, vol 5, pp 3427–3430
Zurück zum Zitat Ahalt SC, Krishnamurthy AK, Chen P, Melton DE (1990) Competitive learning algorithms for vector quantization. Neural Netw 3:277–290CrossRef Ahalt SC, Krishnamurthy AK, Chen P, Melton DE (1990) Competitive learning algorithms for vector quantization. Neural Netw 3:277–290CrossRef
Zurück zum Zitat Alahakoon D, Halgamuge SK, Srinivasan B (2000) Dynamic self organising maps with controlled growth for knowledge discovery. IEEE Trans Neural Netw (Special issue on knowledge discovery and data mining) 11(3):601–614 Alahakoon D, Halgamuge SK, Srinivasan B (2000) Dynamic self organising maps with controlled growth for knowledge discovery. IEEE Trans Neural Netw (Special issue on knowledge discovery and data mining) 11(3):601–614
Zurück zum Zitat Axelson D, Bakken IJ, Gribbestad IS, Ehrnholm B, Nilsen G, Aasly J (2002) Applications of neural network analyses to in vivo 1H magnetic resonance spectroscopy of Parkinson disease patients. J Magn Reson Imaging 16(1):13–20CrossRef Axelson D, Bakken IJ, Gribbestad IS, Ehrnholm B, Nilsen G, Aasly J (2002) Applications of neural network analyses to in vivo 1H magnetic resonance spectroscopy of Parkinson disease patients. J Magn Reson Imaging 16(1):13–20CrossRef
Zurück zum Zitat Ball KD, Erman B, Dill KA (2002) The elastic net algorithm and protein structure prediction. J Comput Chem 23(1):77–83CrossRef Ball KD, Erman B, Dill KA (2002) The elastic net algorithm and protein structure prediction. J Comput Chem 23(1):77–83CrossRef
Zurück zum Zitat Barreto G, Araújo A (2001) Time in self-organizing maps: an overview of models. Int J Comput Res 10(2):139–179 Barreto G, Araújo A (2001) Time in self-organizing maps: an overview of models. Int J Comput Res 10(2):139–179
Zurück zum Zitat Bauer H-U, Villmann T (1997) Growing a hypercubical output space in a self-organizing feature map. IEEE Trans Neural Netw 8(2):218–226CrossRef Bauer H-U, Villmann T (1997) Growing a hypercubical output space in a self-organizing feature map. IEEE Trans Neural Netw 8(2):218–226CrossRef
Zurück zum Zitat Bauer H-U, Der R, Herrmann M (1996) Controlling the magnification factor of self-organizing feature maps. Neural Comput 8:757–771CrossRef Bauer H-U, Der R, Herrmann M (1996) Controlling the magnification factor of self-organizing feature maps. Neural Comput 8:757–771CrossRef
Zurück zum Zitat Benaim M, Tomasini L (1991) Competitive and self-organizing algorithms based on the minimization of an information criterion. In: Proceedings of 1991 international conference in artificial neural networks (ICANN'91). Espoo, Finland. Elsevier Science Publishers, North-Holland, pp 391–396 Benaim M, Tomasini L (1991) Competitive and self-organizing algorithms based on the minimization of an information criterion. In: Proceedings of 1991 international conference in artificial neural networks (ICANN'91). Espoo, Finland. Elsevier Science Publishers, North-Holland, pp 391–396
Zurück zum Zitat Bishop CM (2006) Pattern recognition and machine learning. Springer, New YorkMATH Bishop CM (2006) Pattern recognition and machine learning. Springer, New YorkMATH
Zurück zum Zitat Bishop CM, Svensén M, Williams CKI (1996) GTM: a principled alternative to the self-organizing map. In: Proceedings 1996 International Conference on Artificial Neural Networks (ICANN’96). Bochum, Germany, 16–19 July 1996. Lecture notes in computer science, vol 1112. Springer, pp 165–170 Bishop CM, Svensén M, Williams CKI (1996) GTM: a principled alternative to the self-organizing map. In: Proceedings 1996 International Conference on Artificial Neural Networks (ICANN’96). Bochum, Germany, 16–19 July 1996. Lecture notes in computer science, vol 1112. Springer, pp 165–170
Zurück zum Zitat Bishop CM, Hinton GE, and Strachan IGD (1997) In: Proceedings IEE fifth international conference on artificial neural networks. Cambridge UK, 7–9 July 1997, pp 111–116 Bishop CM, Hinton GE, and Strachan IGD (1997) In: Proceedings IEE fifth international conference on artificial neural networks. Cambridge UK, 7–9 July 1997, pp 111–116
Zurück zum Zitat Bishop CM, Svensén M, Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput 10:215–234CrossRef Bishop CM, Svensén M, Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput 10:215–234CrossRef
Zurück zum Zitat Blackmore J, Miikkulainen R (1993) Incremental grid growing: encoding high-dimensional structure into a two-dimensional feature map. In: Proceedings of IEEE international conference on neural networks. San Francisco, CA. IEEE Press, Piscataway, NJ, vol 1, pp 450–455 Blackmore J, Miikkulainen R (1993) Incremental grid growing: encoding high-dimensional structure into a two-dimensional feature map. In: Proceedings of IEEE international conference on neural networks. San Francisco, CA. IEEE Press, Piscataway, NJ, vol 1, pp 450–455
Zurück zum Zitat Bruske J, Sommer G (1995) Dynamic cell structure learns perfectly topology preserving map. Neural Comput 7(4):845–865CrossRef Bruske J, Sommer G (1995) Dynamic cell structure learns perfectly topology preserving map. Neural Comput 7(4):845–865CrossRef
Zurück zum Zitat Carreira-Perpiñán MÁ, Renals S (1998) Dimensionality reduction of electropalatographic data using latent variable models. Speech Commun 26(4):259–282CrossRef Carreira-Perpiñán MÁ, Renals S (1998) Dimensionality reduction of electropalatographic data using latent variable models. Speech Commun 26(4):259–282CrossRef
Zurück zum Zitat Chappell G, Taylor J (1993) The temporal Kohonen map. Neural Netw 6:441–445CrossRef Chappell G, Taylor J (1993) The temporal Kohonen map. Neural Netw 6:441–445CrossRef
Zurück zum Zitat Chinrungrueng C, Séquin CH (1995) Optimal adaptive k-means algorithm with dynamic adjustment of learning rate. IEEE Trans Neural Netw 6:157–169CrossRef Chinrungrueng C, Séquin CH (1995) Optimal adaptive k-means algorithm with dynamic adjustment of learning rate. IEEE Trans Neural Netw 6:157–169CrossRef
Zurück zum Zitat Cottrell M, Fort JC (1987) Etude d’un processus d’auto-organization. Ann Inst Henri Poincaré 23:1–20MathSciNetMATH Cottrell M, Fort JC (1987) Etude d’un processus d’auto-organization. Ann Inst Henri Poincaré 23:1–20MathSciNetMATH
Zurück zum Zitat Deleus FF, Van Hulle MM (2001) Science and technology interactions discovered with a new topographic map-based visualization tool. In: Proceedings of 7th ACM SIGKDD international conference on knowledge discovery in data mining. San Francisco, 26–29 August 2001. ACM Press, New York, pp 42–50 Deleus FF, Van Hulle MM (2001) Science and technology interactions discovered with a new topographic map-based visualization tool. In: Proceedings of 7th ACM SIGKDD international conference on knowledge discovery in data mining. San Francisco, 26–29 August 2001. ACM Press, New York, pp 42–50
Zurück zum Zitat Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood for incomplete data via the EM algorithm. J R Stat Soc B 39:1–38MathSciNetMATH Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood for incomplete data via the EM algorithm. J R Stat Soc B 39:1–38MathSciNetMATH
Zurück zum Zitat Der R, Herrmann M (1993) Phase transitions in self-organizing feature maps. In: Proceedings of 1993 international conference on artificial neuron networks (ICANN'93). Amsterdam, The Netherlands, 13–16 September 1993, Springer, New York, pp 597–600 Der R, Herrmann M (1993) Phase transitions in self-organizing feature maps. In: Proceedings of 1993 international conference on artificial neuron networks (ICANN'93). Amsterdam, The Netherlands, 13–16 September 1993, Springer, New York, pp 597–600
Zurück zum Zitat DeSieno D (1988) Adding a conscience to competitive learning. In: Proceedings of IEEE international conference on neural networks. San Diego, CA, IEEE Press, New York, vol I, pp 117–124 DeSieno D (1988) Adding a conscience to competitive learning. In: Proceedings of IEEE international conference on neural networks. San Diego, CA, IEEE Press, New York, vol I, pp 117–124
Zurück zum Zitat Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689–691CrossRef Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689–691CrossRef
Zurück zum Zitat Durbin R, Szeliski R, Yuille AL (1989) An analysis of the elastic net approach to the traveling salesman problem. Neural Comput 1:348–358CrossRef Durbin R, Szeliski R, Yuille AL (1989) An analysis of the elastic net approach to the traveling salesman problem. Neural Comput 1:348–358CrossRef
Zurück zum Zitat Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47–55CrossRefMATH Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47–55CrossRefMATH
Zurück zum Zitat Euliano NR, Principe JC (1999). A spatiotemporal memory based on SOMs with activity diffusion. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, The Netherlands, pp 253–266CrossRef Euliano NR, Principe JC (1999). A spatiotemporal memory based on SOMs with activity diffusion. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, The Netherlands, pp 253–266CrossRef
Zurück zum Zitat Fritzke B (1994) Growing cell structures – a self-organizing network for unsupervised and supervised learning. Neural Netw 7(9):1441–1460CrossRef Fritzke B (1994) Growing cell structures – a self-organizing network for unsupervised and supervised learning. Neural Netw 7(9):1441–1460CrossRef
Zurück zum Zitat Fritzke B (1995a) A growing neural gas network learns topologies. In: Tesauro G, Touretzky DS, Leen TK (eds) Advances in neural information proceedings systems 7 (NIPS 1994). MIT Press, Cambridge, MA, pp 625–632 Fritzke B (1995a) A growing neural gas network learns topologies. In: Tesauro G, Touretzky DS, Leen TK (eds) Advances in neural information proceedings systems 7 (NIPS 1994). MIT Press, Cambridge, MA, pp 625–632
Zurück zum Zitat Fritzke B (1995b) Growing grid – a self-organizing network with constant neighborhood range and adaptation strength. Neural Process Lett 2(5):9–13CrossRef Fritzke B (1995b) Growing grid – a self-organizing network with constant neighborhood range and adaptation strength. Neural Process Lett 2(5):9–13CrossRef
Zurück zum Zitat Fritzke B (1996) Growing self-organizing networks – why? In: European symposium on artificial neural networks (ESANN96). Bruges, Belgium, 1996. D Facto Publications, Brussels, Belgium, pp 61–72 Fritzke B (1996) Growing self-organizing networks – why? In: European symposium on artificial neural networks (ESANN96). Bruges, Belgium, 1996. D Facto Publications, Brussels, Belgium, pp 61–72
Zurück zum Zitat Gautama T, Van Hulle MM (2006) Batch map extensions of the kernel-based maximum entropy learning rule. IEEE Trans Neural Netw 16(2):529–532CrossRef Gautama T, Van Hulle MM (2006) Batch map extensions of the kernel-based maximum entropy learning rule. IEEE Trans Neural Netw 16(2):529–532CrossRef
Zurück zum Zitat Gersho A, Gray RM (1991) Vector quantization and signal compression. Kluwer, Boston, MA/Dordrecht Gersho A, Gray RM (1991) Vector quantization and signal compression. Kluwer, Boston, MA/Dordrecht
Zurück zum Zitat Geszti T (1990) Physical models of neural networks. World Scientific Press, SingaporeMATH Geszti T (1990) Physical models of neural networks. World Scientific Press, SingaporeMATH
Zurück zum Zitat Gilson SJ, Middleton I, Damper RI (1997) A localised elastic net technique for lung boundary extraction from magnetic resonance images. In: Proceedings of fifth international conference on artificial neural networks. Cambridge, UK, 7–9 July 1997. Mascarenhas Publishing, Stevenage, UK, pp 199–204 Gilson SJ, Middleton I, Damper RI (1997) A localised elastic net technique for lung boundary extraction from magnetic resonance images. In: Proceedings of fifth international conference on artificial neural networks. Cambridge, UK, 7–9 July 1997. Mascarenhas Publishing, Stevenage, UK, pp 199–204
Zurück zum Zitat Gorbunov S, Kisel I (2006) Elastic net for stand-alone RICH ring finding. Nucl Instrum Methods Phys Res A 559:139–142CrossRef Gorbunov S, Kisel I (2006) Elastic net for stand-alone RICH ring finding. Nucl Instrum Methods Phys Res A 559:139–142CrossRef
Zurück zum Zitat Graepel T, Burger M, Obermayer K (1997) Phase transitions in stochastic self-organizing maps. Phys Rev E 56(4):3876–3890CrossRef Graepel T, Burger M, Obermayer K (1997) Phase transitions in stochastic self-organizing maps. Phys Rev E 56(4):3876–3890CrossRef
Zurück zum Zitat Graepel T, Burger M, Obermayer K (1998) Self-organizing maps: generalizations and new optimization techniques. Neurocomputing 21:173–190CrossRefMATH Graepel T, Burger M, Obermayer K (1998) Self-organizing maps: generalizations and new optimization techniques. Neurocomputing 21:173–190CrossRefMATH
Zurück zum Zitat Grossberg S (1976) Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors. Biol Cybern 23:121–134MathSciNetCrossRefMATH Grossberg S (1976) Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors. Biol Cybern 23:121–134MathSciNetCrossRefMATH
Zurück zum Zitat Günter S, Bunke H (2002) Self-organizing map for clustering in the graph domain, Pattern Recog Lett 23:415–417CrossRef Günter S, Bunke H (2002) Self-organizing map for clustering in the graph domain, Pattern Recog Lett 23:415–417CrossRef
Zurück zum Zitat Hagenbuchner M, Sperduti A, Tsoi AC (2003) A self-organizing map for adaptive processing of structured data. IEEE Trans Neural Netw 14(3):491–505CrossRef Hagenbuchner M, Sperduti A, Tsoi AC (2003) A self-organizing map for adaptive processing of structured data. IEEE Trans Neural Netw 14(3):491–505CrossRef
Zurück zum Zitat Hammer B, Micheli A, Strickert M, Sperduti A (2004) A general framework for unsupervised processing of structured data. Neurocomputing 57:3–35CrossRef Hammer B, Micheli A, Strickert M, Sperduti A (2004) A general framework for unsupervised processing of structured data. Neurocomputing 57:3–35CrossRef
Zurück zum Zitat Hammer B, Micheli A, Neubauer N, Sperduti A, Strickert M (2005) Self organizing maps for time series. In: Proceedings of WSOM 2005. Paris, France, 5–8 September 2005, pp 115–122 Hammer B, Micheli A, Neubauer N, Sperduti A, Strickert M (2005) Self organizing maps for time series. In: Proceedings of WSOM 2005. Paris, France, 5–8 September 2005, pp 115–122
Zurück zum Zitat Heskes T (2001) Self-organizing maps, vector quantization, and mixture modeling. IEEE Trans Neural Netw 12(6):1299–1305CrossRef Heskes T (2001) Self-organizing maps, vector quantization, and mixture modeling. IEEE Trans Neural Netw 12(6):1299–1305CrossRef
Zurück zum Zitat Heskes TM, Kappen B (1993) Error potentials for self-organization. In: Proceedings of IEEE international conference on neural networks. San Francisco, CA. IEEE Press, Piscataway, NJ, pp 1219–1223 Heskes TM, Kappen B (1993) Error potentials for self-organization. In: Proceedings of IEEE international conference on neural networks. San Francisco, CA. IEEE Press, Piscataway, NJ, pp 1219–1223
Zurück zum Zitat Jin B, Zhang Y-Q, Wang B (2005) Evolutionary granular kernel trees and applications in drug activity comparisons, In: Proceedings of the 2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB’05). San Diego, CA, 14–15 November 2005, IEEE Press, Piscataway, NY, pp 1–6 Jin B, Zhang Y-Q, Wang B (2005) Evolutionary granular kernel trees and applications in drug activity comparisons, In: Proceedings of the 2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB’05). San Diego, CA, 14–15 November 2005, IEEE Press, Piscataway, NY, pp 1–6
Zurück zum Zitat Kabán A (2005) A scalable generative topographic mapping for sparse data sequences. In: Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC’05). Las Vegas, NV, 4–6 April 2005. IEEE Computer Society, vol 1, pp 51–56 Kabán A (2005) A scalable generative topographic mapping for sparse data sequences. In: Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC’05). Las Vegas, NV, 4–6 April 2005. IEEE Computer Society, vol 1, pp 51–56
Zurück zum Zitat Kass M, Witkin A, Terzopoulos D (1987) Active contour models. Int J Comput Vis 1(4):321–331CrossRef Kass M, Witkin A, Terzopoulos D (1987) Active contour models. Int J Comput Vis 1(4):321–331CrossRef
Zurück zum Zitat Kangas J (1990) Time-delayed self-organizing maps. In: Proceedings IEEE/INNS international Joint Conference on neural networks 1990. San Diego, CA, IEEE, New York, vol 2, pp 331–336 Kangas J (1990) Time-delayed self-organizing maps. In: Proceedings IEEE/INNS international Joint Conference on neural networks 1990. San Diego, CA, IEEE, New York, vol 2, pp 331–336
Zurück zum Zitat Kaski S, Honkela T, Lagus K, Kohonen T (1998) WEBSOM – self-organizing maps of document collections. Neurocomputing 21:101–117CrossRefMATH Kaski S, Honkela T, Lagus K, Kohonen T (1998) WEBSOM – self-organizing maps of document collections. Neurocomputing 21:101–117CrossRefMATH
Zurück zum Zitat Kim YK, Ra JB (1995) Adaptive learning method in self-organizing map for edge preserving vector quantization. IEEE Trans Neural Netw 6:278–280CrossRef Kim YK, Ra JB (1995) Adaptive learning method in self-organizing map for edge preserving vector quantization. IEEE Trans Neural Netw 6:278–280CrossRef
Zurück zum Zitat Kitamoto A (2002) Evolution map: modeling state transition of typhoon image sequences by spatio-temporal clustering. Lect Notes Comput Sci 2534/2002: 283–290CrossRef Kitamoto A (2002) Evolution map: modeling state transition of typhoon image sequences by spatio-temporal clustering. Lect Notes Comput Sci 2534/2002: 283–290CrossRef
Zurück zum Zitat Kohonen T (1984) Self-organization and associative memory. Springer, HeidelbergMATH Kohonen T (1984) Self-organization and associative memory. Springer, HeidelbergMATH
Zurück zum Zitat Kohonen T (1991) Self-organizing maps: optimization approaches. In: Kohonen T, Mäkisara K, Simula O, Kangas J (eds) Artificial neural networks. North-Holland, Amsterdam, pp 981–990 Kohonen T (1991) Self-organizing maps: optimization approaches. In: Kohonen T, Mäkisara K, Simula O, Kangas J (eds) Artificial neural networks. North-Holland, Amsterdam, pp 981–990
Zurück zum Zitat Kohonen T (1995) Self-organizing maps, 2nd edn. Springer, Heidelberg Kohonen T (1995) Self-organizing maps, 2nd edn. Springer, Heidelberg
Zurück zum Zitat Kohonen T (1997) Self-organizing maps. Springer Kohonen T (1997) Self-organizing maps. Springer
Zurück zum Zitat Kohonen T, Somervuo P (1998) Self-organizing maps on symbol strings. Neurocomputing 21:19–30CrossRefMATH Kohonen T, Somervuo P (1998) Self-organizing maps on symbol strings. Neurocomputing 21:19–30CrossRefMATH
Zurück zum Zitat Kohonen T, Kaski S, Salojärvi J, Honkela J, Paatero V, Saarela A (1999) Self organization of a massive document collection. IEEE Trans Neural Netw 11(3): 574–585CrossRef Kohonen T, Kaski S, Salojärvi J, Honkela J, Paatero V, Saarela A (1999) Self organization of a massive document collection. IEEE Trans Neural Netw 11(3): 574–585CrossRef
Zurück zum Zitat Koskela T, Varsta M, Heikkonen J, Kaski K (1998) Recurrent SOM with local linear models in time series prediction. In: Verleysen M (ed) Proceedings of 6th European symposium on artificial neural networks (ESANN 1998). Bruges, Belgium, April 22–24, 1998. D-Facto, Brussels, Belgium, pp 167–172 Koskela T, Varsta M, Heikkonen J, Kaski K (1998) Recurrent SOM with local linear models in time series prediction. In: Verleysen M (ed) Proceedings of 6th European symposium on artificial neural networks (ESANN 1998). Bruges, Belgium, April 22–24, 1998. D-Facto, Brussels, Belgium, pp 167–172
Zurück zum Zitat Kostiainen T, Lampinen J (2002) Generative probability density model in the self-organizing map. In: Seiffert U, Jain L (eds) Self-organizing neural networks: Recent advances and applications. Physica-Verlag, Heidelberg, pp 75–94 Kostiainen T, Lampinen J (2002) Generative probability density model in the self-organizing map. In: Seiffert U, Jain L (eds) Self-organizing neural networks: Recent advances and applications. Physica-Verlag, Heidelberg, pp 75–94
Zurück zum Zitat Laaksonen J, Koskela M, Oja E (2002) PicSOM–self-organizing image retrieval with MPEG-7 content descriptors. IEEE Trans Neural Netw 13(4):841–853CrossRef Laaksonen J, Koskela M, Oja E (2002) PicSOM–self-organizing image retrieval with MPEG-7 content descriptors. IEEE Trans Neural Netw 13(4):841–853CrossRef
Zurück zum Zitat Lin JK, Grier DG, Cowan JD (1997) Faithful representation of separable distributions. Neural Comput 9:1305–1320CrossRef Lin JK, Grier DG, Cowan JD (1997) Faithful representation of separable distributions. Neural Comput 9:1305–1320CrossRef
Zurück zum Zitat Linsker R (1988) Self-organization in a perceptual network. Computer 21:105–117CrossRef Linsker R (1988) Self-organization in a perceptual network. Computer 21:105–117CrossRef
Zurück zum Zitat Linsker R (1989) How to generate ordered maps by maximizing the mutual information between input and output signals. Neural Comput 1:402–411CrossRef Linsker R (1989) How to generate ordered maps by maximizing the mutual information between input and output signals. Neural Comput 1:402–411CrossRef
Zurück zum Zitat Luttrell SP (1989) Self-organization: a derivation from first principles of a class of learning algorithms. In: Proceedings IEEE international joint conference on neural networks (IJCNN89). Washington, DC, Part I, IEEE Press, Piscataway, NJ, pp 495–498 Luttrell SP (1989) Self-organization: a derivation from first principles of a class of learning algorithms. In: Proceedings IEEE international joint conference on neural networks (IJCNN89). Washington, DC, Part I, IEEE Press, Piscataway, NJ, pp 495–498
Zurück zum Zitat Luttrell SP (1990) Derivation of a class of training algorithms. IEEE Trans Neural Netw 1:229–232CrossRef Luttrell SP (1990) Derivation of a class of training algorithms. IEEE Trans Neural Netw 1:229–232CrossRef
Zurück zum Zitat Luttrell SP (1991) Code vector density in topographic mappings: scalar case. IEEE Trans Neural Netw 2:427–436CrossRef Luttrell SP (1991) Code vector density in topographic mappings: scalar case. IEEE Trans Neural Netw 2:427–436CrossRef
Zurück zum Zitat Martinetz TM (1993) Competitive Hebbian learning rule forms perfectly topology preserving maps. In: Proceedings of international conference on artificial neural networks (ICANN93). Amsterdam, The Netherlands, 13–16 September 1993. Springer, London, pp 427–434 Martinetz TM (1993) Competitive Hebbian learning rule forms perfectly topology preserving maps. In: Proceedings of international conference on artificial neural networks (ICANN93). Amsterdam, The Netherlands, 13–16 September 1993. Springer, London, pp 427–434
Zurück zum Zitat Martinetz T, Schulten K (1991) A “neural-gas” network learns topologies. In: Kohonen T, Mäkisara K, Simula O, Kangas J (eds) Proceedings of International Conference on Artificial Neural Networks (ICANN-91). Espoo, Finland, 24–28 June 1991, vol I, North-Holland, Amsterdam, The Netherlands, pp 397–402 Martinetz T, Schulten K (1991) A “neural-gas” network learns topologies. In: Kohonen T, Mäkisara K, Simula O, Kangas J (eds) Proceedings of International Conference on Artificial Neural Networks (ICANN-91). Espoo, Finland, 24–28 June 1991, vol I, North-Holland, Amsterdam, The Netherlands, pp 397–402
Zurück zum Zitat Martinetz T, Berkovich S, Schulten K (1993) “Neural-gas” network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4(4):558–569CrossRef Martinetz T, Berkovich S, Schulten K (1993) “Neural-gas” network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4(4):558–569CrossRef
Zurück zum Zitat Merkl D, He S, Dittenbach M, Rauber A (2003) Adaptive hierarchical incremental grid growing: an architecture for high-dimensional data visualization. In: Proceedings of 4th workshop on self-organizing maps (WSOM03). Kitakyushu, Japan, 11–14 September 2003 Merkl D, He S, Dittenbach M, Rauber A (2003) Adaptive hierarchical incremental grid growing: an architecture for high-dimensional data visualization. In: Proceedings of 4th workshop on self-organizing maps (WSOM03). Kitakyushu, Japan, 11–14 September 2003
Zurück zum Zitat Mulier F, Cherkassky V (1995) Self-organization as an iterative kernel smoothing process. Neural Comput 7:1165–1177CrossRef Mulier F, Cherkassky V (1995) Self-organization as an iterative kernel smoothing process. Neural Comput 7:1165–1177CrossRef
Zurück zum Zitat Rauber A, Merkl D, Dittenbach M (2002) The growing hierarchical self-organizing map: exploratory analysis of high-dimensional data. IEEE Trans Neural Netw 13(6):1331–1341CrossRef Rauber A, Merkl D, Dittenbach M (2002) The growing hierarchical self-organizing map: exploratory analysis of high-dimensional data. IEEE Trans Neural Netw 13(6):1331–1341CrossRef
Zurück zum Zitat Risi S, Mörchen F, Ultsch A, Lewark P (2007) Visual mining in music collections with emergent SOM. In: Proceedings of workshop on self-organizing maps (WSOM ’07). Bielefeld, Germany, September 3–6, 2007, ISBN: 978-3-00-022473-7, CD ROM, available online at http://biecoll.ub.uni-bielefeld.de Risi S, Mörchen F, Ultsch A, Lewark P (2007) Visual mining in music collections with emergent SOM. In: Proceedings of workshop on self-organizing maps (WSOM ’07). Bielefeld, Germany, September 3–6, 2007, ISBN: 978-3-00-022473-7, CD ROM, available online at http://​biecoll.​ub.​uni-bielefeld.​de
Zurück zum Zitat Ritter H (1991) Asymptotic level density for a class of vector quantization processes. IEEE Trans Neural Netw 2(1):173–175MathSciNetCrossRef Ritter H (1991) Asymptotic level density for a class of vector quantization processes. IEEE Trans Neural Netw 2(1):173–175MathSciNetCrossRef
Zurück zum Zitat Ritter H (1998) Self-organizing maps in non-Euclidean spaces. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 97–108 Ritter H (1998) Self-organizing maps in non-Euclidean spaces. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 97–108
Zurück zum Zitat Ritter H, Kohonen T (1989) Self-organizing semantic maps. Biol Cybern 61:241–254CrossRef Ritter H, Kohonen T (1989) Self-organizing semantic maps. Biol Cybern 61:241–254CrossRef
Zurück zum Zitat Ritter H, Schulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping. Biol Cybern 54:99–106CrossRefMATH Ritter H, Schulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping. Biol Cybern 54:99–106CrossRefMATH
Zurück zum Zitat Ritter H, Schulten K (1988) Kohonen's self-organizing maps: exploring their computational capabilities, In: Proceedings of IEEE international conference on neural networks (ICNN). San Diego, CA. IEEE, New York, vol I, pp 109–116 Ritter H, Schulten K (1988) Kohonen's self-organizing maps: exploring their computational capabilities, In: Proceedings of IEEE international conference on neural networks (ICNN). San Diego, CA. IEEE, New York, vol I, pp 109–116
Zurück zum Zitat Ritter H, Martinetz T, Schulten K (1992) Neural computation and self-organizing maps: an introduction. Addison-Wesley, Reading, MAMATH Ritter H, Martinetz T, Schulten K (1992) Neural computation and self-organizing maps: an introduction. Addison-Wesley, Reading, MAMATH
Zurück zum Zitat Rose K, Gurewitz E, Fox GC (1993) Constrained clustering as an optimization method. IEEE Trans Pattern Anal Mach Intell 15(8):785–794CrossRef Rose K, Gurewitz E, Fox GC (1993) Constrained clustering as an optimization method. IEEE Trans Pattern Anal Mach Intell 15(8):785–794CrossRef
Zurück zum Zitat Schulz R, Reggia JA (2004) Temporally asymmetric learning supports sequence processing in multi-winner self-organizing maps. Neural Comput 16(3):535–561CrossRefMATH Schulz R, Reggia JA (2004) Temporally asymmetric learning supports sequence processing in multi-winner self-organizing maps. Neural Comput 16(3):535–561CrossRefMATH
Zurück zum Zitat Seo S, Obermayer K (2004) Self-organizing maps and clustering methods for matrix data. Neural Netw 17(8–9):1211–1229CrossRefMATH Seo S, Obermayer K (2004) Self-organizing maps and clustering methods for matrix data. Neural Netw 17(8–9):1211–1229CrossRefMATH
Zurück zum Zitat Shawe-Taylor J, Cristianini N (2004) Kernel methods in computational biology. MIT Press, Cambridge, MA Shawe-Taylor J, Cristianini N (2004) Kernel methods in computational biology. MIT Press, Cambridge, MA
Zurück zum Zitat Simon G, Lendasse A, Cottrell M, Fort J-C, Verleysen M (2003) Double SOM for long-term time series prediction. In: Proceedings of the workshop on self-organizing maps (WSOM 2003). Hibikino, Japan, September 11–14, 2003, pp 35–40 Simon G, Lendasse A, Cottrell M, Fort J-C, Verleysen M (2003) Double SOM for long-term time series prediction. In: Proceedings of the workshop on self-organizing maps (WSOM 2003). Hibikino, Japan, September 11–14, 2003, pp 35–40
Zurück zum Zitat Somervuo PJ (2004) Online algorithm for the self-organizing map of symbol strings. Neural Netw 17(8–9):1231–1240CrossRef Somervuo PJ (2004) Online algorithm for the self-organizing map of symbol strings. Neural Netw 17(8–9):1231–1240CrossRef
Zurück zum Zitat Steil JJ, Sperduti A (2007) Indices to evaluate self-organizing maps for structures. In: Proceedings of the workshop on self-organizing maps (WSOM07) Bielefeld, Germany, 3–6 September 2007. CD ROM, 2007, available online at http://biecoll.ub.uni-bielefeld.de Steil JJ, Sperduti A (2007) Indices to evaluate self-organizing maps for structures. In: Proceedings of the workshop on self-organizing maps (WSOM07) Bielefeld, Germany, 3–6 September 2007. CD ROM, 2007, available online at http://​biecoll.​ub.​uni-bielefeld.​de
Zurück zum Zitat Strickert M, Hammer B (2003a) Unsupervised recursive sequence processing, In: Verleysen M (ed) European Symposium on Artificial Neural Networks (ESANN 2003). Bruges, Belgium, 23–25 April 2003. D-Side Publications, Evere, Belgium, pp 27–32 Strickert M, Hammer B (2003a) Unsupervised recursive sequence processing, In: Verleysen M (ed) European Symposium on Artificial Neural Networks (ESANN 2003). Bruges, Belgium, 23–25 April 2003. D-Side Publications, Evere, Belgium, pp 27–32
Zurück zum Zitat Strickert M, Hammer B (2003b) Neural gas for sequences. In: Proceedings of the workshop on self-organizing maps (WSOM’03). Hibikino, Japan, September 2003, pp 53–57 Strickert M, Hammer B (2003b) Neural gas for sequences. In: Proceedings of the workshop on self-organizing maps (WSOM’03). Hibikino, Japan, September 2003, pp 53–57
Zurück zum Zitat Strickert M, Hammer B (2005) Merge SOM for temporal data. Neurocomputing 64:39–72CrossRef Strickert M, Hammer B (2005) Merge SOM for temporal data. Neurocomputing 64:39–72CrossRef
Zurück zum Zitat Tiňo P, Nabney I (2002) Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way. IEEE Trans Pattern Anal Mach Intell 24(5):639–656CrossRef Tiňo P, Nabney I (2002) Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way. IEEE Trans Pattern Anal Mach Intell 24(5):639–656CrossRef
Zurück zum Zitat Tiňo P, Kabán A, Sun Y (2004) A generative probabilistic approach to visualizing sets of symbolic sequences. In: Kohavi R, Gehrke J, DuMouchel W, Ghosh J (eds) Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining (KDD-2004), Seattle, WA, 22–25 August 2004. ACM Press, New York, pp 701–706 Tiňo P, Kabán A, Sun Y (2004) A generative probabilistic approach to visualizing sets of symbolic sequences. In: Kohavi R, Gehrke J, DuMouchel W, Ghosh J (eds) Proceedings of the tenth ACM SIGKDD international conference on knowledge discovery and data mining (KDD-2004), Seattle, WA, 22–25 August 2004. ACM Press, New York, pp 701–706
Zurück zum Zitat Tolat V (1990) An analysis of Kohonen's self-organizing maps using a system of energy functions. Biol Cybern 64:155–164CrossRefMATH Tolat V (1990) An analysis of Kohonen's self-organizing maps using a system of energy functions. Biol Cybern 64:155–164CrossRefMATH
Zurück zum Zitat Ultsch A, Siemon HP (1990) Kohonen's self organizing feature maps for exploratory data analysis. In: Proceedings international neural networks. Kluwer, Paris, pp 305–308 Ultsch A, Siemon HP (1990) Kohonen's self organizing feature maps for exploratory data analysis. In: Proceedings international neural networks. Kluwer, Paris, pp 305–308
Zurück zum Zitat Ultsch A, Mörchen F (2005) ESOM-Maps: Tools for clustering, visualization, and classification with emergent SOM. Technical Report No. 46, Department of Mathematics and Computer Science, University of Marburg, Germany Ultsch A, Mörchen F (2005) ESOM-Maps: Tools for clustering, visualization, and classification with emergent SOM. Technical Report No. 46, Department of Mathematics and Computer Science, University of Marburg, Germany
Zurück zum Zitat Ueda N, Nakano R (1993) A new learning approach based on equidistortion principle for optimal vector quantizer design. In: Proceedings of IEEE NNSP93, Linthicum Heights, MD. IEEE, Piscataway, NJ, pp 362–371 Ueda N, Nakano R (1993) A new learning approach based on equidistortion principle for optimal vector quantizer design. In: Proceedings of IEEE NNSP93, Linthicum Heights, MD. IEEE, Piscataway, NJ, pp 362–371
Zurück zum Zitat Van den Bout DE, Miller TK III (1989) TInMANN: the integer Markovian artificial neural network. In: Proceedings of international joint conference on neural networks (IJCNN89). Washington, DC, 18–22 June 1989, Erlbaum, Englewood Chifts, NJ, pp II205–II211 Van den Bout DE, Miller TK III (1989) TInMANN: the integer Markovian artificial neural network. In: Proceedings of international joint conference on neural networks (IJCNN89). Washington, DC, 18–22 June 1989, Erlbaum, Englewood Chifts, NJ, pp II205–II211
Zurück zum Zitat Van Hulle MM (1997a) Topology-preserving map formation achieved with a purely local unsupervised competitive learning rule. Neural Netw 10(3): 431–446CrossRef Van Hulle MM (1997a) Topology-preserving map formation achieved with a purely local unsupervised competitive learning rule. Neural Netw 10(3): 431–446CrossRef
Zurück zum Zitat Van Hulle MM (1997b) Nonparametric density estimation and regression achieved with topographic maps maximizing the information-theoretic entropy of their outputs. Biol Cybern 77:49–61CrossRefMATH Van Hulle MM (1997b) Nonparametric density estimation and regression achieved with topographic maps maximizing the information-theoretic entropy of their outputs. Biol Cybern 77:49–61CrossRefMATH
Zurück zum Zitat Van Hulle MM (1998) Kernel-based equiprobabilistic topographic map formation. Neural Comput 10(7):1847–1871CrossRef Van Hulle MM (1998) Kernel-based equiprobabilistic topographic map formation. Neural Comput 10(7):1847–1871CrossRef
Zurück zum Zitat Van Hulle MM (2000) Faithful representations and topographic maps: from distortion- to information-based self-organization. Wiley, New York Van Hulle MM (2000) Faithful representations and topographic maps: from distortion- to information-based self-organization. Wiley, New York
Zurück zum Zitat Van Hulle MM (2002a) Kernel-based topographic map formation by local density modeling. Neural Comput 14(7):1561–1573CrossRefMATH Van Hulle MM (2002a) Kernel-based topographic map formation by local density modeling. Neural Comput 14(7):1561–1573CrossRefMATH
Zurück zum Zitat Van Hulle MM (2002b) Joint entropy maximization in kernel-based topographic maps. Neural Comput 14(8):1887–1906 Van Hulle MM (2002b) Joint entropy maximization in kernel-based topographic maps. Neural Comput 14(8):1887–1906
Zurück zum Zitat Van Hulle MM (2005a) Maximum likelihood topographic map formation. Neural Comput 17(3):503–513CrossRefMATH Van Hulle MM (2005a) Maximum likelihood topographic map formation. Neural Comput 17(3):503–513CrossRefMATH
Zurück zum Zitat Van Hulle MM (2005b) Edgeworth-expanded topographic map formation. In: Proceedings of workshop on self-organizing maps (WSOM05). Paris, France, 5–8 September 2005, pp 719–724 Van Hulle MM (2005b) Edgeworth-expanded topographic map formation. In: Proceedings of workshop on self-organizing maps (WSOM05). Paris, France, 5–8 September 2005, pp 719–724
Zurück zum Zitat Van Hulle MM (2009) Kernel-based topographic maps: theory and applications. In: Wah BW (ed) Encyclopedia of computer science and engineering. Wiley, Hoboken, vol 3, pp 1633–1650 Van Hulle MM (2009) Kernel-based topographic maps: theory and applications. In: Wah BW (ed) Encyclopedia of computer science and engineering. Wiley, Hoboken, vol 3, pp 1633–1650
Zurück zum Zitat Van Hulle MM, Gautama T (2004) Optimal smoothing of kernel-based topographic maps with application to density-based clustering of shapes. J VLSI Signal Proces Syst Signal, Image, Video Technol 37:211–222CrossRef Van Hulle MM, Gautama T (2004) Optimal smoothing of kernel-based topographic maps with application to density-based clustering of shapes. J VLSI Signal Proces Syst Signal, Image, Video Technol 37:211–222CrossRef
Zurück zum Zitat Verbeek JJ, Vlassis N, Kröse BJA (2005) Self-organizing mixture models. Neurocomputing 63:99–123CrossRef Verbeek JJ, Vlassis N, Kröse BJA (2005) Self-organizing mixture models. Neurocomputing 63:99–123CrossRef
Zurück zum Zitat Vesanto J (1997) Using the SOM and local models in time-series prediction. In: Proceedings of workshop on self-organizing maps (WSOM 1997). Helsinki, Finland, 4–6 June 1997. Helsinki University of Technology, Espoo, Finland, pp 209–214 Vesanto J (1997) Using the SOM and local models in time-series prediction. In: Proceedings of workshop on self-organizing maps (WSOM 1997). Helsinki, Finland, 4–6 June 1997. Helsinki University of Technology, Espoo, Finland, pp 209–214
Zurück zum Zitat Voegtlin T (2002) Recursive self-organizing maps. Neural Netw 15(8–9):979–992CrossRef Voegtlin T (2002) Recursive self-organizing maps. Neural Netw 15(8–9):979–992CrossRef
Zurück zum Zitat Wiemer JC (2003) The time-organized map algorithm: extending the self-organizing map to spatiotemporal signals. Neural Comput 15(5):1143–1171CrossRefMATH Wiemer JC (2003) The time-organized map algorithm: extending the self-organizing map to spatiotemporal signals. Neural Comput 15(5):1143–1171CrossRefMATH
Zurück zum Zitat Willshaw DJ, von der Malsburg C (1976) How patterned neural connections can be set up by self-organization. Proc Roy Soc Lond B 194:431–445 Willshaw DJ, von der Malsburg C (1976) How patterned neural connections can be set up by self-organization. Proc Roy Soc Lond B 194:431–445
Zurück zum Zitat Yin H, Allinson NM (2001) Self-organizing mixture networks for probability density estimation. IEEE Trans Neural Netw 12:405–411CrossRef Yin H, Allinson NM (2001) Self-organizing mixture networks for probability density estimation. IEEE Trans Neural Netw 12:405–411CrossRef
Metadaten
Titel
Self-organizing Maps
verfasst von
Marc M. Van Hulle
Copyright-Jahr
2012
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-540-92910-9_19