Vector Bundles for Data Alignment and Dimensionality Reduction

Explore vector bundles and their applications in data science through this 54-minute conference talk by Jose Perea. Delve into the rich structure of vector bundles as families of vector spaces parametrized by topological spaces, and discover their role in solving synchronization problems. Learn how classical machinery like classifying maps and characteristic classes can be adapted for algorithms and noisy data. Examine topology-preserving dimensionality reduction problems and their solutions through embedding the total space of data bundles. Gain insights into applications in computational chemistry and dynamical systems, with specific examples including cryo-EM, configuration space of pentane, and the Torus Double Gyre Attractor. Access additional resources through provided arXiv links for further study on this advanced topic in applied algebraic topology.

Intro
Vector Bundles for Data Analysis and Dimensionality
Vector bundles (Definition)
Vector bundles (examples)
Vector bundles (From Cocycles)
cryo-EM: Cryogenic Electron Microscop
Example: Configuration space of pentane
Example: Torus Double Gyre Attractor