SOMM – Self-Organized Manifold Mapping

  • Edson Caoru Kitani
  • Emilio Del-Moral-Hernandez
  • Leandro A. Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7553)


The Self Organizing Map (SOM) [1] proposed by Kohonen has proved to be remarkable in terms of its range of applications. It can be used for high dimensional space visualization, pattern recognition, input space dimensionality reduction and for generating prototyping to extrapolate information. Basically, tasks conducted by the SOM method are closely related with input space mapping in order to preserve topological and metric relationship between samples. These maps are meant to create a low dimensional output representation of high dimensional input space. Although maps higher than two dimensions can be created by SOM, it is common to work with the limit of one or two dimensions. This work presents a methodology named SOMM (Self-Organized Manifold Mapping) that can be useful to discover structures and clusters of input dataset using the SOM map as a representation of data distribution structure.


Manifold Learning Self Organizing Maps Dimensionality Reduction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kohonen, T.: Self-organization and associative memory. Springer-Verlag New York, Inc., New York (1989)CrossRefGoogle Scholar
  2. 2.
    Mayer, R., Rauber, A.: Visualising Clusters in Self-Organising Maps with Minimum Spanning Trees. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010, Part II. LNCS, vol. 6353, pp. 426–431. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Pölzbauer, G., Rauber, A., Dittenbach, M.: Graph projection techniques for self-organizing maps. In: ESANN 2005 European Symposium on Artificial Neural Networks, Bruges, pp. 533–538 (2005)Google Scholar
  4. 4.
    Ultsch, A.: Maps for the visualization of high-dimensional data spaces. In: Proc. of Workshop of Self Organizing Maps, pp. 225–228 (2003)Google Scholar
  5. 5.
    Sammon Jr., J.W.: A nonlinear mapping for data structure analysis. IEEE Transaction on Computers, 401–409 (1969)Google Scholar
  6. 6.
    Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science Magazine 290, 2319–2323 (2000)Google Scholar
  7. 7.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by local linear embedding. Science Magazine 290, 2323–2326 (2000)Google Scholar
  8. 8.
    Kitani, E.C., Del-Moral-Hernandez, E., Giraldi, A.G., Thomaz, C.E.: Exploring and understanding the high dimensional and sparse image face space: A self or-ganized manifold mapping. New approaches to characterization and recognition of faces, pp. 225–238. Intech Open Access Publisher (2011)Google Scholar
  9. 9.
    Brugger, D., Bogdan, M., Rosenstiel, W.: Automatic cluster detection in Koho-nen’s SOM. IEEE Transaction on Neural Networks 19(3), 442–459 (2008)CrossRefGoogle Scholar
  10. 10.
    Bauer, H.U., Pawelzik, K.R.: Quantifying the neighborhood preservation of Self-Organizing Feature Maps. IEEE Transaction on Neural Networks 3(4), 570–579 (1992)CrossRefGoogle Scholar
  11. 11.
    Kiviluoto, K.: Topology preservation in self-organizing maps. In: IEEE International Conference on Neural Networks, vol. 1, pp. 294–299 (1996)Google Scholar
  12. 12.
    Kitani, E.C., Del-Moral-Hernandez, E., Thomaz, C.E., Silva, L.A.: Visual inter-pretation of Self Organizing Maps. In: IEEE-CS 11th Brazilian Symposium on Neural Networks (SBRN), pp. 37–42. São Bernardo do Campo (2010)Google Scholar
  13. 13.
    Cormen, T.H., et al.: Introduction to algorithms, 2nd edn. MIT Press (2001)Google Scholar
  14. 14.
    Vesanto, J., et al.: SOM Toolbox for Matlab 5. Helsinki University of Technology, Helsinki, pp. 1-60. Report A57 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Edson Caoru Kitani
    • 1
  • Emilio Del-Moral-Hernandez
    • 1
  • Leandro A. Silva
    • 2
  1. 1.Polytechnic SchoolUniversity of Sao PauloBrazil
  2. 2.School of Computing and InformaticsMackenzie Presbyterian UniversityBrazil

Personalised recommendations