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Topological pattern recognition for point cloud data

delete2014-05-12
delete152
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OA
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G
Gunnar Carlsson *
DOI：10.1017/S0962492914000051delete
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Abstract

Abstract

En 中文
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.
Keywords:
PROBE WMAP OBSERVATIONS
PERSISTENT COSMIC WEB
LARGE-SCALE STRUCTURE
FILAMENTARY STRUCTURE
PROBABILITY
STATISTICS
HOMOLOGY
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Journal

Acta Numerica cover
Acta Numerica
IF:
11.3
Papers:
89
Citations:
3.4K

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