## Statistical Topological Data Analysis using Persistence Landscapes

*Peter Bubenik*; 16(Jan):77−102, 2015.

### Abstract

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.

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