2024/10/16 by Ryan Murray, Murray, Ryan, Adam Pickarski +1 · 1 citation
Medicine · #68Q25 #68R10 #68U05 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Lung Cancer Treatments and Mutations #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Imaging and Pathology Studies #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2410.13063
openalex publication_date 2024/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 → ∞. We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.