Parametric UMAP embeddings for representation and semi-supervised learning

Understand

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.