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Self-organizing Maps

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Handbook of Natural Computing

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.

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References

  • 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

    Google Scholar 

  • Ahalt SC, Krishnamurthy AK, Chen P, Melton DE (1990) Competitive learning algorithms for vector quantization. Neural Netw 3:277–290

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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):13–20

    Article  Google Scholar 

  • Ball KD, Erman B, Dill KA (2002) The elastic net algorithm and protein structure prediction. J Comput Chem 23(1):77–83

    Article  Google Scholar 

  • Barreto G, Araújo A (2001) Time in self-organizing maps: an overview of models. Int J Comput Res 10(2):139–179

    Google Scholar 

  • Bauer H-U, Villmann T (1997) Growing a hypercubical output space in a self-organizing feature map. IEEE Trans Neural Netw 8(2):218–226

    Article  Google Scholar 

  • Bauer H-U, Der R, Herrmann M (1996) Controlling the magnification factor of self-organizing feature maps. Neural Comput 8:757–771

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Bishop CM (2006) Pattern recognition and machine learning. Springer, New York

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Bishop CM, Svensén M, Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput 10:215–234

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Bruske J, Sommer G (1995) Dynamic cell structure learns perfectly topology preserving map. Neural Comput 7(4):845–865

    Article  Google Scholar 

  • Carreira-Perpiñán MÁ, Renals S (1998) Dimensionality reduction of electropalatographic data using latent variable models. Speech Commun 26(4):259–282

    Article  Google Scholar 

  • Centre NNR (2003) Bibliography on the Self-Organizing Map (SOM) and Learning Vector Quantization (LVQ), Helsinki University of Technology. http://liinwww.ira.uka.de/bibliography/Neural/SOM.LVQ.html

  • Chappell G, Taylor J (1993) The temporal Kohonen map. Neural Netw 6:441–445

    Article  Google Scholar 

  • Chinrungrueng C, Séquin CH (1995) Optimal adaptive k-means algorithm with dynamic adjustment of learning rate. IEEE Trans Neural Netw 6:157–169

    Article  Google Scholar 

  • Cottrell M, Fort JC (1987) Etude d’un processus d’auto-organization. Ann Inst Henri Poincaré 23:1–20

    MathSciNet  MATH  Google Scholar 

  • D’Alimonte D, Lowe D, Nabney IT, Sivaraksa M (2005) Visualising uncertain data. In: Proceedings European conference on emergent aspects in clinical data analysis (EACDA2005). Pisa, Italy, 28–30 September 2005. http://ciml.di.unipi.it/EACDA2005/papers.html

  • 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

    Google Scholar 

  • Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood for incomplete data via the EM algorithm. J R Stat Soc B 39:1–38

    MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Durbin R, Willshaw D (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature 326:689–691

    Article  Google Scholar 

  • Durbin R, Szeliski R, Yuille AL (1989) An analysis of the elastic net approach to the traveling salesman problem. Neural Comput 1:348–358

    Article  Google Scholar 

  • Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: ordering, convergence properties and energy functions. Biol Cybern 67:47–55

    Article  MATH  Google Scholar 

  • 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 253–266

    Chapter  Google Scholar 

  • Fritzke B (1994) Growing cell structures – a self-organizing network for unsupervised and supervised learning. Neural Netw 7(9):1441–1460

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Fritzke B (1995b) Growing grid – a self-organizing network with constant neighborhood range and adaptation strength. Neural Process Lett 2(5):9–13

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Gautama T, Van Hulle MM (2006) Batch map extensions of the kernel-based maximum entropy learning rule. IEEE Trans Neural Netw 16(2):529–532

    Article  Google Scholar 

  • Gersho A, Gray RM (1991) Vector quantization and signal compression. Kluwer, Boston, MA/Dordrecht

    Google Scholar 

  • Geszti T (1990) Physical models of neural networks. World Scientific Press, Singapore

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • Gorbunov S, Kisel I (2006) Elastic net for stand-alone RICH ring finding. Nucl Instrum Methods Phys Res A 559:139–142

    Article  Google Scholar 

  • Graepel T, Burger M, Obermayer K (1997) Phase transitions in stochastic self-organizing maps. Phys Rev E 56(4):3876–3890

    Article  Google Scholar 

  • Graepel T, Burger M, Obermayer K (1998) Self-organizing maps: generalizations and new optimization techniques. Neurocomputing 21:173–190

    Article  MATH  Google Scholar 

  • Grossberg S (1976) Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors. Biol Cybern 23:121–134

    Article  MathSciNet  MATH  Google Scholar 

  • Günter S, Bunke H (2002) Self-organizing map for clustering in the graph domain, Pattern Recog Lett 23:415–417

    Article  Google Scholar 

  • Hagenbuchner M, Sperduti A, Tsoi AC (2003) A self-organizing map for adaptive processing of structured data. IEEE Trans Neural Netw 14(3):491–505

    Article  Google Scholar 

  • Hammer B, Micheli A, Strickert M, Sperduti A (2004) A general framework for unsupervised processing of structured data. Neurocomputing 57:3–35

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Heskes T (2001) Self-organizing maps, vector quantization, and mixture modeling. IEEE Trans Neural Netw 12(6):1299–1305

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Kass M, Witkin A, Terzopoulos D (1987) Active contour models. Int J Comput Vis 1(4):321–331

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Kaski S, Honkela T, Lagus K, Kohonen T (1998) WEBSOM – self-organizing maps of document collections. Neurocomputing 21:101–117

    Article  MATH  Google Scholar 

  • Kim YK, Ra JB (1995) Adaptive learning method in self-organizing map for edge preserving vector quantization. IEEE Trans Neural Netw 6:278–280

    Article  Google Scholar 

  • Kitamoto A (2002) Evolution map: modeling state transition of typhoon image sequences by spatio-temporal clustering. Lect Notes Comput Sci 2534/2002: 283–290

    Article  Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69

    Article  MathSciNet  MATH  Google Scholar 

  • Kohonen T (1984) Self-organization and associative memory. Springer, Heidelberg

    MATH  Google Scholar 

  • 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

    Google Scholar 

  • Kohonen T (1995) Self-organizing maps, 2nd edn. Springer, Heidelberg

    Google Scholar 

  • Kohonen T (1997) Self-organizing maps. Springer

    Google Scholar 

  • Kohonen T, Somervuo P (1998) Self-organizing maps on symbol strings. Neurocomputing 21:19–30

    Article  MATH  Google Scholar 

  • 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): 574–585

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Laaksonen J, Koskela M, Oja E (2002) PicSOM–self-organizing image retrieval with MPEG-7 content descriptors. IEEE Trans Neural Netw 13(4):841–853

    Article  Google Scholar 

  • Lin JK, Grier DG, Cowan JD (1997) Faithful representation of separable distributions. Neural Comput 9:1305–1320

    Article  Google Scholar 

  • Linsker R (1988) Self-organization in a perceptual network. Computer 21:105–117

    Article  Google Scholar 

  • Linsker R (1989) How to generate ordered maps by maximizing the mutual information between input and output signals. Neural Comput 1:402–411

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Luttrell SP (1990) Derivation of a class of training algorithms. IEEE Trans Neural Netw 1:229–232

    Article  Google Scholar 

  • Luttrell SP (1991) Code vector density in topographic mappings: scalar case. IEEE Trans Neural Netw 2:427–436

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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):558–569

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Mulier F, Cherkassky V (1995) Self-organization as an iterative kernel smoothing process. Neural Comput 7:1165–1177

    Article  Google Scholar 

  • 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):1331–1341

    Article  Google Scholar 

  • Redner RA, Walker HF (1984) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev 26(2):195–239

    Article  MathSciNet  MATH  Google Scholar 

  • 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

  • Ritter H (1991) Asymptotic level density for a class of vector quantization processes. IEEE Trans Neural Netw 2(1):173–175

    Article  MathSciNet  Google Scholar 

  • Ritter H (1998) Self-organizing maps in non-Euclidean spaces. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 97–108

    Google Scholar 

  • Ritter H, Kohonen T (1989) Self-organizing semantic maps. Biol Cybern 61:241–254

    Article  Google Scholar 

  • Ritter H, Schulten K (1986) On the stationary state of Kohonen's self-organizing sensory mapping. Biol Cybern 54:99–106

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Ritter H, Martinetz T, Schulten K (1992) Neural computation and self-organizing maps: an introduction. Addison-Wesley, Reading, MA

    MATH  Google Scholar 

  • Rose K, Gurewitz E, Fox GC (1993) Constrained clustering as an optimization method. IEEE Trans Pattern Anal Mach Intell 15(8):785–794

    Article  Google Scholar 

  • Schulz R, Reggia JA (2004) Temporally asymmetric learning supports sequence processing in multi-winner self-organizing maps. Neural Comput 16(3):535–561

    Article  MATH  Google Scholar 

  • Seo S, Obermayer K (2004) Self-organizing maps and clustering methods for matrix data. Neural Netw 17(8–9):1211–1229

    Article  MATH  Google Scholar 

  • Shawe-Taylor J, Cristianini N (2004) Kernel methods in computational biology. MIT Press, Cambridge, MA

    Google Scholar 

  • 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

    Google Scholar 

  • Somervuo PJ (2004) Online algorithm for the self-organizing map of symbol strings. Neural Netw 17(8–9):1231–1240

    Article  Google Scholar 

  • 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

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Strickert M, Hammer B (2005) Merge SOM for temporal data. Neurocomputing 64:39–72

    Article  Google Scholar 

  • 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):639–656

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Tolat V (1990) An analysis of Kohonen's self-organizing maps using a system of energy functions. Biol Cybern 64:155–164

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Van Hulle MM (1997a) Topology-preserving map formation achieved with a purely local unsupervised competitive learning rule. Neural Netw 10(3): 431–446

    Article  Google Scholar 

  • Van Hulle MM (1997b) Nonparametric density estimation and regression achieved with topographic maps maximizing the information-theoretic entropy of their outputs. Biol Cybern 77:49–61

    Article  MATH  Google Scholar 

  • Van Hulle MM (1998) Kernel-based equiprobabilistic topographic map formation. Neural Comput 10(7):1847–1871

    Article  Google Scholar 

  • Van Hulle MM (2000) Faithful representations and topographic maps: from distortion- to information-based self-organization. Wiley, New York

    Google Scholar 

  • Van Hulle MM (2002a) Kernel-based topographic map formation by local density modeling. Neural Comput 14(7):1561–1573

    Article  MATH  Google Scholar 

  • Van Hulle MM (2002b) Joint entropy maximization in kernel-based topographic maps. Neural Comput 14(8):1887–1906

    Google Scholar 

  • Van Hulle MM (2005a) Maximum likelihood topographic map formation. Neural Comput 17(3):503–513

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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 37:211–222

    Article  Google Scholar 

  • Verbeek JJ, Vlassis N, Kröse BJA (2005) Self-organizing mixture models. Neurocomputing 63:99–123

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Voegtlin T (2002) Recursive self-organizing maps. Neural Netw 15(8–9):979–992

    Article  Google Scholar 

  • Wiemer JC (2003) The time-organized map algorithm: extending the self-organizing map to spatiotemporal signals. Neural Comput 15(5):1143–1171

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Yin H, Allinson NM (2001) Self-organizing mixture networks for probability density estimation. IEEE Trans Neural Netw 12:405–411

    Article  Google Scholar 

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Acknowledgments

The author is supported by the Excellence Financing program (EF 2005) and the CREA Financing program (CREA/07/027) of K.U.Leuven, the Belgian Fund for Scientific Research – Flanders (G.0234.04 and G.0588.09), the Flemish Regional Ministry of Education (Belgium) (GOA 2000/11), the Belgian Science Policy (IUAP P6/29), and the European Commission (NEST-2003-012963, STREP-2002-016276, IST-2004-027017, and ICT-2007-217077).

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  1. Laboratorium voor Neurofysiologie, K.U. Leuven, Leuven, Belgium

    Marc M. Van Hulle

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  1. LIACS, Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Computer Science Department, University of Colorado, Boulder, USA

    Grzegorz Rozenberg

  3. LIACS, Leiden University, Leiden, The Netherlands

    Thomas Bäck

  4. LIACS, Leiden University, Leiden, The Netherlands

    Joost N. Kok

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Van Hulle, M.M. (2012). Self-organizing Maps. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_19

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