Large data limits and scaling laws for tSNE
Statistics Theory
2024-10-18 v1 Machine Learning
Analysis of PDEs
Machine Learning
Statistics Theory
Abstract
This work considers large-data asymptotics for t-distributed stochastic neighbor embedding (tSNE), a widely-used non-linear dimension reduction algorithm. We identify an appropriate continuum limit of the tSNE objective function, which can be viewed as a combination of a kernel-based repulsion and an asymptotically-vanishing Laplacian-type regularizer. As a consequence, we show that embeddings of the original tSNE algorithm cannot have any consistent limit as . We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.
Cite
@article{arxiv.2410.13063,
title = {Large data limits and scaling laws for tSNE},
author = {Ryan Murray and Adam Pickarski},
journal= {arXiv preprint arXiv:2410.13063},
year = {2024}
}