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Pattern Analysis and Applications

, Volume 17, Issue 2, pp 223–248 | Cite as

Topology-oriented self-organizing maps: a survey

  • César A. AstudilloEmail author
  • B. John Oommen
Survey

Abstract

The self-organizing map (SOM) is a prominent neural network model that has found wide application in a spectrum of domains. Accordingly, it has received widespread attention both from the communities of researchers and practitioners. As a result, several variations of the basic architecture have been devised, specifically in the early years of the SOM’s evolution, which were introduced so as to address various architectural shortcomings or to explore other structures of the basic model. The overall goal of this survey is to present a comprehensive comparison of these networks, in terms of their primitive components and properties. We dichotomize these schemes as being either tree based or non-tree based. We have embarked on this venture with the hope that since the survey is comprehensive and the bibliography extensive, it will be an asset and resource for future researchers.

Keywords

Self-organizing maps Hierarchical SOM SOM Variants Survey 

Notes

Acknowledgments

We record our gratitude to the Associate Editor and anonymous referees of the original version of this paper for their painstaking reviews. The changes that they requested certainly improved the quality of this paper. The work of César A. Astudillo was partially supported by the FONDECYT Grant 11121350, Chile. The work of B. John Oommen was partially supported by NSERC, the Natural Sciences and Engineering Research Council of Canada.

References

  1. 1.
    Alahakoon D, Halgamuge SK, Srinivasan B (2000) Dynamic self-organizing maps with controlled growth for knowledge discovery. IEEE Trans Neural Netw 11(3):601–614CrossRefGoogle Scholar
  2. 2.
    Arsuaga Uriarte E, Díaz Martín F (2005) Topology preservation in SOM. Int J Appl Math Comput Sci 1(1):19–22Google Scholar
  3. 3.
    Astudillo CA, Oommen BJ (2009) On using adaptive binary search trees to enhance self organizing maps. In: Nicholson A, Li X (eds) 22nd Australasian joint conference on artificial intelligence (AI), pp 199–209Google Scholar
  4. 4.
    Astudillo CA, Oommen BJ (2011) Imposing tree-based topologies onto self organizing maps. Inf Sci 181(18):3798–3815MathSciNetCrossRefGoogle Scholar
  5. 5.
    Astudillo CA, Oommen BJ (2013) On achieving semi-supervised pattern recognition by utilizing tree-based SOMs. Pattern Recognit 46(1):293–304Google Scholar
  6. 6.
    Astudillo CA, Oommen BJ (2014) Self-organizing maps whose topologies can be learned with adaptive binary search trees using conditional rotations. Pattern Recognit 47(1):96–113CrossRefGoogle Scholar
  7. 7.
    Bacciu D, Micheli A, Sperduti A (2010) Compositional generative mapping of structured data. In: Proceedings of the international joint conference on neural networks (IJCNN), pp 1–8Google Scholar
  8. 8.
    Bacciu D, Micheli A, Sperduti A (2012) Compositional generative mapping for tree-structured data—part I: bottom-up probabilistic modeling of trees. IEEE Trans Neural Netw Learn Syst 23(12):1987–2002CrossRefGoogle Scholar
  9. 9.
    Bacciu D, Micheli A, Sperduti A (2013) Compositional generative mapping for tree-structured data—part II: topographic projection model. IEEE Trans Neural Netw Learn Syst 24(2):231–247CrossRefGoogle Scholar
  10. 10.
    Bauer HU, Herrmann M, Villmann T (1999) Neural maps and topographic vector quantization. Neural Netw 12(4–5):659–676CrossRefGoogle Scholar
  11. 11.
    Bauer HU, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. Neural Netw 3(4):570–579CrossRefGoogle Scholar
  12. 12.
    Berglund E, Sitte J (2006) The parameterless self-organizing map algorithm. Neural Netw IEEE Trans 17(2):305–316CrossRefGoogle Scholar
  13. 13.
    Bishop CM, Svensén M, Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput 10(1):215–234CrossRefGoogle Scholar
  14. 14.
    Bishop CM, Svensén M, Williams CKI (1996) GTM: a principled alternative to the self-organizing map. In: Proceedings of the 1996 international conference on artificial neural networks (ICANN’96). Springer, London, pp 165–170Google Scholar
  15. 15.
    Blackmore J (1995) Visualizing high-dimensional structure with the incremental grid growing neural network. Master’s thesis, University of Texas at AustinGoogle Scholar
  16. 16.
    Budinich M (1995) On the ordering conditions for self-organizing maps. Neural Comput 7(2):284–289CrossRefGoogle Scholar
  17. 17.
    Campos MM, Carpenter GA (2001) S-tree: self-organizing trees for data clustering and online vector quantization. Neural Netw 14(4–5):505 – 525CrossRefGoogle Scholar
  18. 18.
    Carpenter GA, Grossberg S (1988) The art of adaptive pattern recognition by a self-organizing neural network. Computer 21(3):77–88CrossRefGoogle Scholar
  19. 19.
    Cheetham RP, Oommen BJ, Ng DTH (1993) Adaptive structuring of binary search trees using conditional rotations. IEEE Trans Knowl Data Eng 5(4):695–704CrossRefGoogle Scholar
  20. 20.
    Chow TWS, Rahman MKM (2009) Multilayer SOM with tree-structured data for efficient document retrieval and plagiarism detection. Neural Netw IEEE Trans 20(9):1385–1402CrossRefGoogle Scholar
  21. 21.
    Conti PL, De Giovanni L (1991) On the mathematical treatment of self organization: extension of some classical results. Int Conf Artif Neural Netw ICANN 2:1089–1812Google Scholar
  22. 22.
    Corona F, Mulas M, Baratti R, Romagnoli JA (2010) On the topological modeling and analysis of industrial process data using the SOM. Comput Chem Eng 34(12):2022–2032. doi: 10.1016/j.compchemeng.2010.07.002
  23. 23.
    Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39(1):1–38zbMATHMathSciNetGoogle Scholar
  24. 24.
    DeSieno D (1988) Adding a conscience to competitive learning. IEEE Int Conf Neural Netw 1:117–124CrossRefGoogle Scholar
  25. 25.
    Dittenbach M, Merkl D, Rauber A (2000) The growing hierarchical self-organizing map. In: Proceedings of the IEEE-INNS-ENNS international joint conference on neural networks (IJCNN), vol 6, pp 15–19Google Scholar
  26. 26.
    Dopazo J (2007) Fundamentals of data mining in genomics and proteomics, chapter clustering—class discovery in the post-genomic era. Springer, US, pp 123–148Google Scholar
  27. 27.
    Dopazo J, Carazo JM (1997) Phylogenetic reconstruction using an unsupervised growing neural network that adopts the topology of a phylogenetic tree. J Mol Evol 44(2):226–233CrossRefGoogle Scholar
  28. 28.
    Duda R, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley-Interscience, USAGoogle Scholar
  29. 29.
    Forti A, Foresti GL (2006) Growing hierarchical tree SOM: an unsupervised neural network with dynamic topology. Neural Netw 19(10):1568–1580zbMATHCrossRefGoogle Scholar
  30. 30.
    Fritzke B (1991) Unsupervised clustering with growing cell structures. In: IJCNN-91-seattle international joint conference on neural networks, vol 2, pp 531–536Google Scholar
  31. 31.
    Fritzke B (1994) Growing cell structures—a self-organizing network for unsupervised and supervised learning. Neural Netw 7(9):1441–1460CrossRefGoogle Scholar
  32. 32.
    Fritzke B (1995) Growing grid—a self-organizing network with constant neighborhood range and adaptation strength. Neural Process Lett 2(5):9–13CrossRefGoogle Scholar
  33. 33.
    Fritzke B (1995) A growing neural gas network learns topologies. In: Tesauro G, Touretzky DS, Leen TK (eds) Advances in neural information processing systems, vol 7. MIT Press, Cambridge, pp 625–632Google Scholar
  34. 34.
    Fuertes J, Domínguez M, Díaz I, Prada M, Morán A, Alonso S (2012) Visualization maps based on SOM to analyze MIMO systems. Neural Comput Appl 1–13. doi: 10.1007/s00521-012-1090-3
  35. 35.
    Furukawa T (2009) SOM of SOMs. Neural Netw 22(4):463–478CrossRefGoogle Scholar
  36. 36.
    Greene D, Cunningham P, Mayer R (2008) Machine learning techniques for multimedia: case studies on organization and retrieval (cognitive technologies), chapter unsupervised learning and clustering. Springer, Berlin, pp 51–90Google Scholar
  37. 37.
    Guan L (2006) Self-organizing trees and forests: a powerful tool in pattern clustering and recognition. In: Campilho A, Kamel M (eds) Image analysis and recognition. Proceedings of the 3rd international conference, ICIAR 2006, Póvoa de Varzim, Portugal, September 18–20, 2006. Lecture notes in computer science, vol 4141. Springer, Berlin, pp 1–14Google Scholar
  38. 38.
    Hagenbuchner M, Sperduti A, Tsoi AC (2009) Graph self-organizing maps for cyclic and unbounded graphs. Neurocomputing 72(79):1419–1430. Advances in machine learning and computational intelligence 16th European symposium on artificial neural networks 2008Google Scholar
  39. 39.
    Hagenbuchner M, Sperduti A, Chung Tsoi A (2003) A self-organizing map for adaptive processing of structured data. IEEE Trans Neural Netw 14(3):491–505CrossRefGoogle Scholar
  40. 40.
    Haykin S (2008) Neural networks and learning machines, 3rd edn. Prentice Hall, USAGoogle Scholar
  41. 41.
    Heskes T (1999) Energy functions for self-organizing maps. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 303–315Google Scholar
  42. 42.
    Huang G, Babri HA, Li H (1998) Ordering of self-organizing maps in multi-dimensional cases. Neural Comput 10:19–24CrossRefGoogle Scholar
  43. 43.
    Iwasaki Y, Wada K, Itoh M, Ikemura T, Abe T (2011) A novel bioinformatics strategy to predict directional changes of influenza a virus genome sequences. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 198–206Google Scholar
  44. 44.
    Kaski S, Kangas J, Kohonen T (1998) Bibliography of self-organizing map (SOM) papers: 1981–1997. Neural Comput Surv 1:102–350Google Scholar
  45. 45.
    Kiviluoto K (1996) Topology preservation in self-organizing maps. In: IEEE Neural Networks Council (ed) Proceedings of international conference on neural networks (ICNN’96), vol 1, pp 294–299, New Jersey, 1996Google Scholar
  46. 46.
    Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69zbMATHMathSciNetCrossRefGoogle Scholar
  47. 47.
    Kohonen T (1995) Self-organizing maps. Springer, New YorkGoogle Scholar
  48. 48.
    Koikkalainen P, Oja E (1990) Self-organizing hierarchical feature maps. IJCNN Int Joint Conf Neural Netw 2:279–284Google Scholar
  49. 49.
    Maia J, Barreto G, Coelho A (2011) Evolving a self-organizing feature map for visual object tracking. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 121–130Google Scholar
  50. 50.
    Martinetz M, Schulten KJ (1991) A “neural-gas” network learns topologies. In: Proceedings of international conference on articial neural networks, vol I, pp 397–402, North-Holland, 1991Google Scholar
  51. 51.
    Martinetz T, Schulten K (1994) Topology representing networks. Neural Netw 7(3):507–522CrossRefGoogle Scholar
  52. 52.
    Matsuda N, Tokutaka H (2011) Decision of class borders on a spherical som with non-equal class distributions. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 328–337Google Scholar
  53. 53.
    Mehmood Y, Abbas M, Chen X, Honkela T (2011) Self-organizing maps of nutrition, lifestyle and health situation in the world. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 160–167Google Scholar
  54. 54.
    Miikkulainen R (1990) Script recognition with hierarchical feature maps. Connect Sci 2(1, 2):83–101CrossRefGoogle Scholar
  55. 55.
    Oja M, Kaski S, Kohonen T (2003) Bibliography of self-organizing map (SOM) papers: 1998–2001 addendum. Neural Comput Surv 3:1–156Google Scholar
  56. 56.
    Olier I, Vellido A, Giraldo J (2010) Kernel generative topographic mapping. In: European symposium on artificial neural network (ESANN’10), pp 481–486Google Scholar
  57. 57.
    Pakkanen J, Iivarinen J, Oja E (2004) The evolving tree—a novel self-organizing network for data analysis. Neural Process Lett 20(3):199–211CrossRefGoogle Scholar
  58. 58.
    Pampalk E, Widmer G, Chan A (2004) A new approach to hierarchical clustering and structuring of data with self-organizing maps. Intell Data Anal 8(2):131–149Google Scholar
  59. 59.
    Pöllä M, Honkela T, Kohonen T (2009) Bibliography of self-organizing map (SOM) papers: 2002–2005 addendum. Technical report TKK-ICS-R23, Department of Information and Computer Science, Helsinki University of Technology, Espoo, FinlandGoogle Scholar
  60. 60.
    Pölzlbauer G (2004) Survey and comparison of quality measures for self-organizing maps. In: Paralič J, Pölzlbauer G, Rauber A (eds) Proceedings of the fifth workshop on data analysis (WDA’04), pp 67–82. Sliezsky dom, Vysoké Tatry, Slovakia. Elfa Academic Press, Kosice Google Scholar
  61. 61.
    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):1331–1341CrossRefGoogle Scholar
  62. 62.
    Rojas R (1996) Neural networks: a systematic introduction. Springer, New YorkGoogle Scholar
  63. 63.
    Sarlin P, Eklund T (2011) Fuzzy clustering of the self-organizing map: some applications on financial time series. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 40–50Google Scholar
  64. 64.
    Strickert M, Hammer B (2005) Merge SOM for temporal data. Neurocomputing 64(0):39–71. Trends in neurocomputing: 12th European symposium on artificial neural networks 2004Google Scholar
  65. 65.
    Tasdemir K, Merenyi E (2009) Exploiting data topology in visualization and clustering of self-organizing maps. IEEE Trans Neural Netw 20(4):549–562CrossRefGoogle Scholar
  66. 66.
    Tokutaka H, Ohkita M, Hai Y, Fujimura K, Oyabu M (2011) Classification using topologically preserving spherical self-organizing maps. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 308–317Google Scholar
  67. 67.
    Venna J, Kaski S (2001) Neighborhood preservation in nonlinear projection methods: an experimental study. In: Dorffner G, Bischof H, Hornik K (eds) ICANN, vol 2130. Lecture Notes in Computer Science. Springer, Berlin, pp 485–491Google Scholar
  68. 68.
    Vesanto J (1999) SOM-based data visualization methods. Intell Data Anal 3(2):111–126zbMATHCrossRefGoogle Scholar
  69. 69.
    Vesanto J, Himberg J, Alhoniemi E, Parhankangas J (2000) Self-organizing map in matlab: the som toolbox. In: Proceedings of the matlab DSP conference, pp 35–40Google Scholar
  70. 70.
    Villmann T, Der R, Herrmann M, Martinetz TM (1997) Topology preservation in self-organizing feature maps: exact definition and measurement. IEEE Trans Neural Netw 8(2):256–266CrossRefGoogle Scholar
  71. 71.
    Wang Y, Van hamme H (2011) Gaussian selection using self-organizing map for automatic speech recognition. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 218–227Google Scholar
  72. 72.
    Wehrens R, Buydens LMC (2007) Self- and super-organizing maps in R: the Kohonen package. J Stat Softw 21(5):1–19Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversidad de TalcaCuricóChile
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada

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