Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces

Explore the nonembeddability of persistence diagrams into Hilbert spaces in this 27-minute conference talk by Alexander Wagner. Delve into the stability of persistence diagrams and their use as signatures in statistics and machine learning. Examine the family of metrics on persistence diagrams parametrized by a constant p, and investigate the incompatibility of these metrics with inner products. Learn about the necessity of non-trivial feature maps for kernel methods and the distortion of metrics on persistence diagrams. Discover the proof that when p is strictly greater than two, the associated metric space does not coarsely embed into any Hilbert space. Follow the talk's structure, covering introduction, recap, related work, history, isometric embedding, p greater than 2, sketch, Gaussian kernel, future work, and summary.