[2206.01816] Contrastive Learning Unifies $t$-SNE And UMAP - ArXiv

Computer Science > Machine Learning arXiv:2206.01816 (cs) [Submitted on 3 Jun 2022 (v1), last revised 28 Feb 2023 (this version, v2)] Title:From $t$-SNE to UMAP with contrastive learning Authors:Sebastian Damrich (1), Jan Niklas Böhm (2), Fred A. Hamprecht (1), Dmitry Kobak (2) ((1) IWR at Heidelberg University, (2) University of Tübingen) View a PDF of the paper titled From $t$-SNE to UMAP with contrastive learning, by Sebastian Damrich (1) and 4 other authors View PDF

Abstract:Neighbor embedding methods $t$-SNE and UMAP are the de facto standard for visualizing high-dimensional datasets. Motivated from entirely different viewpoints, their loss functions appear to be unrelated. In practice, they yield strongly differing embeddings and can suggest conflicting interpretations of the same data. The fundamental reasons for this and, more generally, the exact relationship between $t$-SNE and UMAP have remained unclear. In this work, we uncover their conceptual connection via a new insight into contrastive learning methods. Noise-contrastive estimation can be used to optimize $t$-SNE, while UMAP relies on negative sampling, another contrastive method. We find the precise relationship between these two contrastive methods and provide a mathematical characterization of the distortion introduced by negative sampling. Visually, this distortion results in UMAP generating more compact embeddings with tighter clusters compared to $t$-SNE. We exploit this new conceptual connection to propose and implement a generalization of negative sampling, allowing us to interpolate between (and even extrapolate beyond) $t$-SNE and UMAP and their respective embeddings. Moving along this spectrum of embeddings leads to a trade-off between discrete / local and continuous / global structures, mitigating the risk of over-interpreting ostensible features of any single embedding. We provide a PyTorch implementation.

Comments:	ICLR 2023. 44 pages, 19 figures. Code at this https URL and this https URL
Subjects:	Machine Learning (cs.LG); Human-Computer Interaction (cs.HC)
Cite as:	arXiv:2206.01816 [cs.LG]
(or arXiv:2206.01816v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2206.01816 Focus to learn more arXiv-issued DOI via DataCite
Journal reference:	ICLR 2023

Submission history

From: Sebastian Damrich [view email] [v1] Fri, 3 Jun 2022 20:50:54 UTC (25,194 KB) [v2] Tue, 28 Feb 2023 17:32:58 UTC (48,699 KB) Full-text links:

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