Learning a Self-organizing Map Model on a Riemannian Manifold

Authors:
D. J. Yu;E. R. Hancock;W. A. Smith
Affiliations:
School of Computer Science, Nanjing University of Science and Technology, China and Department of Computer Science, University of York, UK;Department of Computer Science, University of York, UK;Department of Computer Science, University of York, UK
Venue:
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Year:
2009

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Abstract

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.