Stochastic neighbor embedding (SNE) for dimension reduction and visualization using arbitrary divergences

Authors:
Kerstin Bunte;Sven Haase;Michael Biehl;Thomas Villmann
Affiliations:
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700AK Groningen, The Netherlands and University of Bielefeld, CITEC Center of Excellence, D ...;Department of Mathematics, University of Applied Sciences Mittweida, Germany;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700AK Groningen, The Netherlands;Department of Mathematics, University of Applied Sciences Mittweida, Germany
Venue:
Neurocomputing
Year:
2012

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Abstract

We present a systematic approach to the mathematical treatment of the t-distributed stochastic neighbor embedding (t-SNE) and the stochastic neighbor embedding (SNE) method. This allows an easy adaptation of the methods or exchange of their respective modules. In particular, the divergence which measures the difference between probability distributions in the original and the embedding space can be treated independently from other components like, e.g. the similarity of data points or the data distribution. We focus on the extension for different divergences and propose a general framework based on the consideration of Frechet-derivatives. This way the general approach can be adapted to the user specific needs.