Harnessing Data Geometry for Biomedical Insights

Explore the cutting-edge field of data geometry in biomedical research through this insightful conference talk delivered by Smita Krishnaswamy at the Computational Genomics Summer Institute (CGSI) 2022. Delve into fundamental challenges and concepts such as manifolds, Gaussian curvature, and diffusion operators. Discover how these mathematical principles apply to scientific data, particularly in stem cell development. Learn about spectral clustering, extraction of harmonic features, and density estimation on graphs. Engage with a thought-provoking experiment that demonstrates the practical applications of these concepts in harnessing data geometry for valuable biomedical insights.

Intro
Fundamental challenges
What is a manifold?
Why is this true of scientific data?
Gaussian curvature
Diffusion Operator
Spectral clustering
Extraction of harmonic features
Stem Cell Development
Kantorovich Rubenstein Duality
Density estimation on Graphs
Thought experiment