Persistent homology for random fields and complexes
Robert J. Adler, Omer Bobrowski, Matthew Strom Borman, Eliran Subag, Shmuel Weinberger · Institute of Mathematical Statistics collections · 2010
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices and, in most detail, the algebraic topology of the excursion sets of random fields.