Parametric UMAP Embeddings for Representation and Semisupervised Learning.

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.

Dimensionality reduction for visualizing single-cell data using UMAP.

Advances in single-cell technologies have enabled high-resolution dissection of tissue composition. Several tools for dimensionality reduction are available to analyze the large number of parameters generated in single-cell studies. Recently, a nonlinear dimensionality-reduction technique, uniform manifold approximation and projection (UMAP), was developed for the analysis of any type of high-dimensional data. Here we apply it to biological data, using three well-characterized mass cytometry and single-cell RNA sequencing datasets. Comparing the performance of UMAP with five other tools, we find that UMAP provides the fastest run times, highest reproducibility and the most meaningful organization of cell clusters. The work highlights the use of UMAP for improved visualization and interpretation of single-cell data.