Parametric UMAP embeddings for representation and semi-supervised learning

• URL: http://arxiv.org/abs/2009.12981v4
• Date: Sun, 29 Aug 2021 16:17:30 GMT
• Title: Parametric UMAP embeddings for representation and semi-supervised learning
• Authors: Tim Sainburg, Leland McInnes, Timothy Q Gentner
• Abstract summary: UMAP is a non-parametric graph-based dimensionality reduction algorithm to find low-dimensional embeddings of structured data. We show that Parametric UMAP performs comparably to its non-parametric counterpart while conferring the benefit of a learned parametric mapping. We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semi-supervised learning.
• Score: 0.03823356975862005
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: UMAP is a non-parametric 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) Compute a graphical representation of a dataset (fuzzy simplicial complex), and (2) Through stochastic gradient descent, optimize 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 non-parametric 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 semi-supervised learning by capturing structure in unlabeled data. Google Colab walkthrough: https://colab.research.google.com/drive/1WkXVZ5pnMrm17m0YgmtoNjM_XHdnE5Vp?usp=sharing

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