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Topological pattern recognition for point cloud data*

Published online by Cambridge University Press:  12 May 2014

Gunnar Carlsson
Gunnar Carlsson*
Affiliation:
Department of Mathematics, Stanford University, CA 94305, USA, E-mail: gunnar@math.stanford.edu
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Abstract

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In this paper we discuss the adaptation of the methods of homology from algebraic topology to the problem of pattern recognition in point cloud data sets. The method is referred to as persistent homology, and has numerous applications to scientific problems. We discuss the definition and computation of homology in the standard setting of simplicial complexes and topological spaces, then show how one can obtain useful signatures, called barcodes, from finite metric spaces, thought of as sampled from a continuous object. We present several different cases where persistent homology is used, to illustrate the different ways in which the method can be applied.

Information

Type
Research Article
Information
Acta Numerica , Volume 23 , May 2014 , pp. 289 - 368
Copyright
Copyright © Cambridge University Press 2014 

Footnotes

*

Colour online for monochrome figures available at journals.cambridge.org//anu.

References

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