Multiscale stochastic neighbor embedding: Towards parameter-free dimensionality reduction

Abstract. Stochastic neighbor embedding (SNE) is a method of dimen-sionality reduction that involves softmax similarities measured between all pairs of data points. To build a suitable embedding, SNE tries to repro-duce in a low-dimensional space the similarities that are observed in the high-dimensional data space. Previous work has investigated the immu-nity of such similarities to norm concentration, as well as enhanced cost functions. This paper proposes an additional refinement, in the form of multiscale similarities, namely averages of softmax ratios with decreasing bandwidths. The objective is to maximize the embedding quality at all scales, with a better preservation of both local and global neighborhoods, and also to exempt the user from having to fix a scale arbitrarily. Ex-periments on several data sets show that this multiscale version of SNE, combined with an appropriate cost function (sum of Jensen-Shannon di-vergences), outperforms all previous variants of SNE.