A Riemannian Self-Organizing Map

  • Dongjun Yu
  • Edwin R. Hancock
  • William A. P. Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5716)


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.


Riemannian Manifold Geodesic Distance Facial Surface Underlying Manifold Codebook Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Dongjun Yu
    • 1
    • 2
  • Edwin R. Hancock
    • 2
  • William A. P. Smith
    • 2
  1. 1.School of Computer ScienceNanjing University of Science and TechnologyNanjingChina
  2. 2.Department of Computer ScienceThe University of YorkYorkUK

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