Parametric UMAP Embeddings for Representation and Semisupervised Learning

By Tim Sainburg, Leland McInnes, Timothy Q. Gentner. Neural Computation, 2020

343 citations recorded by the source corpus.

Abstract UMAP is a nonparametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) computing a graphical representation of a data set (fuzzy simplicial complex) and (2) through stochastic gradient descent, optimizing a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that parametric UMAP performs comparably to its nonparametric counterpart while conferring the benefit of a learned parametric mapping (e.g., fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semisupervised learning by capturing structure in unlabeled data.1

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d2a4a1b9b9c22d6b8d26ea9a9c3d8bedd9c9e9e4

How researchers see this paper

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In Artificial Intelligence

1. Weixin Liang
2. James Y. Zou
3. Yongchan Kwon
4. Serena Yeung
5. Yuhui Zhang
6. Li Fei-Fei
7. Zhou Yu
8. Sunipa Dev

In Computational Theory and Mathematics

1. James Y. Zou
2. Serena Yeung

Citations in the corpus

• Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning (2022, positive): “, MSCOCO Caption) via UMAP visualization [41].”