期刊
ACTA NUMERICA
卷 23, 期 -, 页码 289-368出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0962492914000051
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资金
- National Science Foundation
- National Institutes of Health
- Air Force Office of Scientific Research
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1228304] Funding Source: National Science Foundation
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.
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