Revisiting Hyperbolic t-SNE

Abstract

Dimensionality reduction and visualization methods have become an indispensable tool for the exploration of high-dimensional data. In this area t-SNE has established itself as a primary method; providing a means of visualizing high-dimensional data in a way that preserves local neighbourhood structures. However standard t-SNE embeds data into Euclidean space which struggles to capture properties of data that is network-like, tree-like, or contains hierarchies. As an alternative, the use of Hyperbolic space has been proposed to allow for effective embeddings of such data as connections exist between complex networks and Hyperbolic. In addition, Hyperbolic space has been effectively utilized for representing hierarchical relationships.
Given these endeavors, recent works have adapted t-SNE to Hyperbolic space using the Poincaré Disk model resulting in a method that can visually reveal network-like and hierarchical relationships. However, several related works contain an error in their derived gradient. As t-SNE uses the method of gradient descent for optimizing embeddings, this error may lead to incorrect results. In our work we first correct for this error and explore its consequences. One such consequence is that embeddings are strongly pushed outwards in the disk leading to unintelligible results. Since t-SNE uses a t-distribution to model embeddings, we propose the use of a Gaussian distribution instead as it encourages more compact embeddings. Finally we perform experiments comparing each method qualitatively by assessing resulting visualizations, and quantitatively via the PR-metric.