Barcodes: The persistent topology of data 论文

摘要

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— <bold>persistent homology</bold> —and a novel representation of this algebraic characterization— <bold>barcodes</bold> . We sketch an application of these techniques to the classification of natural images.