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. e result is a practical scalable algorithm that applies to real world data. e 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.

Topological data analysis (TDA) (Edelsbrunner & Harer, 2010), (Carlsson, 2009) is a field focused on understanding the shape and structure of data by computing topological descriptors that summarize features as connected components, loops, and voids. TDA has found wide applications across nonlinear time series analysis (

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