Learning a self-organizing map model on a Riemannian manifold. (English) Zbl 1259.68174

Yu, D. J.; Hancock, E. R.; Smith, W. A. P.

Hancock, Edwin R. (ed.) et al., Mathematics of surfaces XIII. 13th IMA international conference York, UK, September 7–9, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-03595-1/pbk). Lecture Notes in Computer Science 5654, 375-390 (2009).

Summary: 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.
For the entire collection see [Zbl 1173.68011].

MSC:

68T05	Learning and adaptive systems in artificial intelligence
58D17	Manifolds of metrics (especially Riemannian)
68T10	Pattern recognition, speech recognition
68U05	Computer graphics; computational geometry (digital and algorithmic aspects)

Keywords:

SOM; Riemannian manifold; manifold learning; pattern recognition