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Statistical topological data analysis using persistence landscapes. (English) Zbl 1337.68221

Summary: We define a new topological summary for data that we call the persistence landscape. Since this summary lies in a vector space, it is easy to combine with tools from statistics and machine learning, in contrast to the standard topological summaries. Viewed as a random variable with values in a Banach space, this summary obeys a strong law of large numbers and a central limit theorem. We show how a number of standard statistical tests can be used for statistical inference using this summary. We also prove that this summary is stable and that it can be used to provide lower bounds for the bottleneck and Wasserstein distances.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
55N35 Other homology theories in algebraic topology
62G99 Nonparametric inference
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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