Title: Sketching Homology and Homology for Sketching
Abstract: Topological Data Analysis offers deformation invariant descriptors that capture the "shape of data", the (persistent) homology groups. While computation of such groups can be performed combinatorially via linear algebraic manipulations of "adjacency"-like matrices, the time and space complexity required deems them impractical for large data volumes and high-dimensional problems. Sketching algorithms provide approximate solutions via "compressing" big-data problems, efficiently. We explore the application of sketching algorithms to improve the computational efficiency of homology, and conversely, we attempt to devise homology preserving "data-reduction" algorithms.