Learning a Self-organizing Map Model on a Riemannian Manifold

  • D. J. Yu
  • E. R. Hancock
  • W. A. P. Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5654)


We generalize the classic self-organizing map (SOM) in flat Euclidean space (linear manifold) onto a Riemannian manifold. Both sequential and batch learning algorithms for the generalized SOM are presented. Compared with the classical SOM, the most novel feature of the generalized SOM is that it can learn the intrinsic topological neighborhood structure of the underlying Riemannian manifold that fits to the input data. We here compared the performance of the generalized SOM and the classical SOM using real 3-Dimensional facial surface normals data. Experimental results show that the generalized SOM outperforms the classical SOM when the data lie on a curved Riemannian manifold.


SOM Riemannian Manifold Manifold Learning Pattern Recognition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • D. J. Yu
    • 1
    • 2
  • E. R. Hancock
    • 2
  • W. A. P. Smith
    • 2
  1. 1.School of Computer ScienceNanjing University of Science and TechnologyChina
  2. 2.Department of Computer ScienceUniversity of YorkUK

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