Mathematical Foundations of the Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization

Apr, 2011

Abstract. In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NE-XOM) for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE). It treats the components, like data similarity measures and neighborhood functions, independently and easily changeable. And it enables the utilization of different divergences, based on the theory of Fréchet derivatives. In this way we propose a new dimension reduction and visualization algorithm, which can be easily adapted to the user specific request and the actual problem

Link

@INPROCEEDINGS{Bunte_ESANN11_SONE,
author = {K. Bunte and F.-M. Schleif and S. Haase and T. Villmann},
title = {Mathematical Foundations of the Self Organized Neighbor Embedding ({SONE}) for Dimension Reduction and Visualization},
booktitle = {Proc. of the  19th "European Symposium on Artificial Neural Networks (ESANN)},
address = {Bruges, Belgium},
year = {2011},
pages = {29--34},
month = {"Apr."},
editor = {M. Verleysen},
publisher = {D-facto Publications},
url = {http://hdl.handle.net/11370/1e2d4af4-09b2-4dc2-b7e1-73ff3cf18925},
abstract = {Abstract. In this paper we propose the generalization of the recently introduced Neighbor Embedding Exploratory Observation Machine (NE-XOM)  for dimension reduction and visualization. We provide a general mathematical framework called Self Organized Neighbor Embedding (SONE). It treats the components, like data similarity measures and neighborhood functions, independently and easily changeable.  And it enables the utilization of different divergences, based on the theory of Fréchet derivatives.  In this way we propose a new dimension reduction and visualization algorithm, which can be easily adapted to the user specific request and the actual problem},
}