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

TL;DR

This paper analyzes the convergence of t-SNE with generalized kernels, proving that it reaches an equilibrium distribution under broad conditions as data size grows.

Contribution

It extends previous convergence results of t-SNE to include generalized kernels, providing a concrete formulation and broader applicability.

Findings

t-SNE converges to an equilibrium distribution with generalized kernels

Convergence holds under certain conditions as data points increase

Extends prior work to a wider class of kernels

Abstract

T-distributed stochastic neighbor embedding (t-SNE) is a well-known algorithm for visualizing high-dimensional data by finding low-dimensional representations. In this paper, we study the convergence of t-SNE with generalized kernels and extend the results of Auffinger and Fletcher in 2023. Our work starts by giving a concrete formulation of generalized input and output kernels. Then we prove that under certain conditions, the t-SNE algorithm converges to an equilibrium distribution for a wide range of input and output kernels as the number of data points diverges.