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

2010

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 Frechet derivatives. In this way we propose a new dimension reduction and visualization algorithm, which can easily adapted to the user specific request and the actual problem

Link

@techreport{kbunteSONE_TR2010,
author = {K. Bunte and S. Haase and M. Biehl and T. Villmann},
title = {{Mathematical Foundations of Self Organized Neighbor Embedding (SONE) for Dimension Reduction and Visualization}},
institution = {Leipzig University},
year = {2010},
type = {},
number = {MLR-03-2010},
address = {},
month = {},
issn = {1865-3960},
key = {},
url = {https://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_03_2010.pdf},
pages = {52--75},
volume = {4},
journal = {mrl},
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 Frechet derivatives.  In this way we propose a new dimension reduction and visualization algorithm, which can easily adapted to the user specific request and the actual problem},
}