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Large data limits and scaling laws for tSNE

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arxiv 2410.13063 v1 pith:24DIRYLH submitted 2024-10-16 math.ST cs.LGmath.APstat.MLstat.TH

classification math.STcs.LGmath.APstat.MLstat.TH
keywords tsnelimitalgorithmconsistentappropriateasymptoticasymptotically-vanishingasymptotics
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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 $n \to \infty$. We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.

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Cited by 1 Pith paper

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

    stat.ML 2025-05 conditional novelty 5.0 of 10

    Generalized t-SNE with radial exponential input kernels and integrable output kernels converges to a compactly supported equilibrium measure when perplexity scales as log(nρ).

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