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

2024/05/27 by Aditya Ravuri, Ravuri, Aditya, Neil D. Lawrence +1 · 2 citations
Computer Science · Engineering · Social Sciences · #Advanced Computing and Algorithms #Advanced Data Compression Techniques #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Wireless Body Area Networks

paper · pdf · doi:10.48550/arxiv.2405.17412

openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction
• Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements

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