European Congress of Mathematics
Kraków, 2 – 7 July, 2012
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(2) Lawrence National Laboratory, Berkeley, USA
Persistent homology is a recent grandchild of homology that has found use in science and engineering as well as in mathematics. This paper surveys the method as well as the applications, neglecting completeness in favor of highlighting ideas and directions.
Keywords: Algebraic topology, homology groups, distance, stability, algorithms, scale, shape analysis, topology repair, high-dimensional data