Self-Organizing Maps on non-euclidean Spaces
نویسنده
چکیده
We propose a new type of Self-Organizing Map (SOM) that is based on discretizations of curved, non-euclidean spaces. As an introductory example, we brieey discuss \spherical SOMs" on tesselations of the sphere for the display of directional data. We then describe the construction of \hyperbolic SOMs", using regular tesselations of the hyperbolic plane, which is a non-euclidean space characterized by constant negative gaussian curvature. The approach is motivated by the recent observation that the geometry of hyperbolic spaces possesses very favourable properties for the mapping of hierarchical data. We conclude with some initial simulation results illustrating some properties of the hyperbolic SOM and discuss a number of issues for future research.
منابع مشابه
Text Categorization and Semantic Browsing with Self-Organizing Maps on Non-euclidean Spaces
This paper introduces a new type of Self-Organizing Map (SOM) for Text Categorization and Semantic Browsing. We propose a “hyperbolic SOM” (HSOM) based on a regular tesselation of the hyperbolic plane, which is a non-euclidean space characterized by constant negative gaussian curvature. This approach is motivated by the observation that hyperbolic spaces possess a geometry where the size of a n...
متن کاملSpecial Issue on Advances in Self-organizing Maps
It has been 17 years since the first Workshop on Self-organizing Maps (WSOM) was held in Helsinki, Finland in 1997, under the leadership of Teuvo Kohonen. The workshop brings together researchers and practitioners in the field of self-organizing systems and related areas. The 9th WSOMwas held for the first time in LatinAmerica, at the Universidad de Chile, Santiago, Chile, on December 2012. Thi...
متن کاملconceive hyperbolic spaces ?
The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal h...
متن کاملCan rodents conceive hyperbolic spaces?
The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet, one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal ...
متن کاملAnomaly Detection Using Self-Organizing Maps-Based K-Nearest Neighbor Algorithm
Self-organizing maps have been used extensively for condition-based maintenance, where quantization errors of test data referring to the self-organizing maps of healthy training data have been used as features. Researchers have used minimum quantization error as a health indicator, which is sensitive to noise in the training data. Some other researchers have used the average of the quantization...
متن کامل