PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Learning a Self-organizing Map Model on a Riemannian Manifold
Dongjun Yu, Edwin Hancock and William Smith
In: IMA Conference on the Mathematics of Surfaces 2009, Sept 7-9, 2009, York, UK.


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.

EPrint Type:Conference or Workshop Item (Oral)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Machine Vision
Theory & Algorithms
ID Code:6868
Deposited By:Edwin Hancock
Deposited On:08 April 2010