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Abstract:
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This poster gives an introduction to the R package TDA and how to do a statistical inference on topological data analysis with the package TDA. The salient topological features of data can be quantified with persistent homology. Between persistent homologies, the bottleneck distance is defined. The bottleneck distance between persistent homologies is bounded by the distance between corresponding functions, which is the stability theorem. Based on the stability theorem, the confidence band can be computed to distinguish significant topological features from noisy features in the persistent homology. This poster illustrates how R package TDA compute preliminary functions, persistent homologies, and confidence bands with examples.
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