Equilibrium Distributions for t-distributed Stochastic Neighbour Embedding

2023/04/07 by Antonio Auffinger, Auffinger, Antonio, Daniel A. Fletcher +1 · 2 citations
Computer Science · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2304.03727

openalex publication_date 2023/04/07 · openalex created_date 2023/04/11 · openalex updated_date 2026/07/28

Abstract

We study the empirical measure of the output of the t-distributed stochastic neighbour embedding algorithm when the initial data is given by n independent, identically distributed inputs. We prove that under certain assumptions on the distribution of the inputs, this sequence of measures converges to an equilibrium distribution, which is described as a solution of a variational problem.

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• t-SNE Exaggerates Clusters, Provably
• Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels

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