The neural representation of space in rats has inspired many navigation systems for robots. In particular, Self-Organizing (Feature) Maps (SOM) are often used to give a sense of location to robots by mapping sensor information to a low-dimensional grid. For example, a robot equipped with a panoramic camera can build a 2D SOM from vectors of landmark bearings. If there are four landmarks in the robot's environment, then the 2D SOM is embedded in a 2D manifold lying in a 4D space. In general, the set of observable sensor vectors form a low-dimensional Riemannian manifold in a high-dimensional space. In a landmark bearing sensor space, the manifold can have a large curvature in some regions (when the robot is near a landmark for example), making the Eulidian distance a very poor approximation of the Riemannian metric. In this paper, we present and compare three methods for measuring the similarity between vectors of landmark bearings. We also discuss a method to equip SOM with a good approximation of the Riemannian metric. Although we illustrate the techniques with a landmark bearing problem, our approach is applicable to other types of data sets. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Keeratipranon, N., & Maire, F. (2005). Bearing similarity measures for self-organizing feature maps. In Lecture Notes in Computer Science (Vol. 3578, pp. 286–293). Springer Verlag. https://doi.org/10.1007/11508069_38
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