Witness complexes and Lagrangian duality
Erik Carlsson (University of California, Davis)
I'll discuss a method for approximating the super-level set persistent homology of a Gaussian kernel density estimator for a point cloud data set, which is related to the witness complex. Instead of selecting elements of the data set, the witnesses are generated using quadratic programming, and the shifted Voronoi diagram (aka the power diagram) of a specific choice of landmark points. Interestingly, issues related to scalability in higher dimensions lead to considering the Lagrangian dual problem of the QP. This is joint work with J. Carlsson.