Leland McInnes

Tim Sainburg, Leland McInnes, Timothy Q Gentner

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

Xin Li, Ondrej E. Dyck, Mark P. Oxley et al.

Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient processing and interpretation of large volumes of data remain challenging, especially for two-dimensional or light materials because the diffraction signal recorded on the pixelated arrays is weak. Here we employ data-driven manifold leaning approaches for straightforward visualization and exploration analysis of the 4D-STEM datasets, distilling real-space neighboring effects on atomically resolved deflection patterns from single-layer graphene, with single dopant atoms, as recorded on a pixelated detector. These extracted patterns relate to both individual atom sites and sublattice structures, effectively discriminating single dopant anomalies via multi-mode views. We believe manifold learning analysis will accelerate physics discoveries coupled between data-rich imaging mechanisms and materials such as ferroelectric, topological spin and van der Waals heterostructures.

Leland McInnes, John Healy, James Melville

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.