A Riemannian Self-Organizing Map

Authors:
Dongjun Yu;Edwin R. Hancock;William A. Smith
Affiliations:
School of Computer Science, Nanjing University of Science and Technology, Nanjing, China 210094 and Department of Computer Science, The University of York, York, UK YO10 5DD;Department of Computer Science, The University of York, York, UK YO10 5DD;Department of Computer Science, The University of York, York, UK YO10 5DD
Venue:
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
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.