Abstract
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— persistent homology —and a novel representation of this algebraic characterization— barcodes . We sketch an application of these techniques to the classification of natural images.
Citation impact
1,282
total citations
- FWCI
- 16.83
- Percentile
- 100%
- References
- 32
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Authors
1Topics & keywords
Topics
Keywords
- Topological data analysis
- Persistent homology
- Point cloud
- Computational topology
- Algebraic topology
- Homology (biology)
- Topology (electrical circuits)
- Computer science
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