Attraction-repulsion swarming: a generalized framework of t-SNE via force normalization and tunable interactions.

We propose a new method for data visualization based on attraction-repulsion swarming (ARS) dynamics, which we call ARS visualization. ARS is a generalized framework that is based on viewing the t-distributed stochastic neighbour embedding (t-SNE) visualization technique as a swarm of interacting agents driven by attraction and repulsion. Motivated by recent developments in swarming, we modify the t-SNE dynamics to include a normalization by the total influence, which results in better posed dynamics in which we can use a data size independent time step (of [Formula: see text]) and a simple gradient descent iteration. ARS also includes the ability to separately tune the attraction and repulsion kernels, which gives the user control over the tightness within clusters and the spacing between them in the visualization. In contrast with t-SNE, our proposed ARS data visualization method is not gradient descent on the Kullback-Leibler (KL) divergence, and can be viewed solely as an interacting particle system driven by attraction and repulsion forces, which illustrates that the KL divergence is not an essential part of the t-SNE algorithm. We provide theoretical results illustrating how the choice of interaction kernel affects the dynamics, and experimental results to validate our method and compare to t-SNE on the MNIST, Cifar-10, SVHN and NORB datasets.This article is part of the theme issue 'Partial differential equations in data science'.