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

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. (C) 2012 Elsevier B.V. All rights reserved.