Persistent Topology of Data and Barcodes
Can barcodes represent the algebraic characterization, persistent homology?
University of Pennsylvania Professor Robert Ghrist thinks they might. He has posted a PDF pre-print of a paper titled Barcodes: The Persistent Topology of Data.
This article surveys recent work of Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in high-dimensional data. The primary mathematical tool considered is a homology theory for point-cloud data sets — persistent homology — and a novel representation of this algebraic characterization
— barcodes. We sketch an application of these techniques to the classification of natural images.
5 internet points to anyone who understands the paper.
