Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels

Abstract

We extend the results by Auffinger and Fletcher in 2023 on the large-sample limit of t-SNE to a broader class of input and output kernels. We prove that under natural assumptions on the input distribution and the decay of the output kernel, if perplexity scales linearly with data size, the empirical measures and values of minimizers converge to an equilibrium distribution. We conclude with numerical examples comparing different kernels.