Math @ Duke
Publications [#199091] of John Harer
- with Yuriy Mileyko, Sayan Mukherjee, Probability measures on the space of persistence diagrams,
Journal of Inverse Problems, vol. 27 no. 12
(last updated on 2011/12/11)
This is a major step forward in the general problem of integrating computational topology and statistics.
This paper shows that the space of persistence diagrams has properties
that allow for the definition of probability measures which support
expectations, variances, percentiles and conditional probabilities.
This provides a theoretical basis for a statistical treatment of
persistence diagrams, for example computing sample averages and sample
variances of persistence diagrams. We first prove that the space of
persistence diagrams with the Wasserstein metric is complete and
separable. We then prove a simple criterion for compactness in this
space. These facts allow us to show the existence of the standard
statistical objects needed to extend the theory of topological
persistence to a much larger set of applications.
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