Large data limits and scaling laws for tSNE
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910654026219520 |
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| author | Murray, Ryan Pickarski, Adam |
| author_facet | Murray, Ryan Pickarski, Adam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large data limits and scaling laws for tSNE Murray, Ryan Pickarski, Adam Statistics Theory Machine Learning Analysis of PDEs 68Q25, 68R10, 68U05 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. |
| title | Large data limits and scaling laws for tSNE |
| topic | Statistics Theory Machine Learning Analysis of PDEs 68Q25, 68R10, 68U05 |
| url | https://arxiv.org/abs/2410.13063 |