Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE

Aditya Ravuri; Neil D. Lawrence

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arXiv · 2405.17412

Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE

Aditya Ravuri·Neil D. Lawrence

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Abstract

This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate of the data precision matrix) using a Wishart distribution, with a mean given by a non-linear covariance function evaluated on the latents. This interpretation offers deeper theoretical and semantic insights into such algorithms, and forging a connection to Gaussian process latent variable models by showing that well-known kernels can be used to describe covariances implied by graph Laplacians. We also introduce tools with which similar dimensionality reduction methods can be studied.

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BibTeX RIS

Aditya Ravuri, Neil D. Lawrence. 2024-05-27. Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE. https://arxiv.org/abs/2405.17412

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