Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Convergence of Persistence Landscapes and Silhouettes   Persistent homology is a widely used tool in Topological Data Analysis that
encodes multiscale topological information as a multi-set of points in the
plane called a persistence diagram. It is difficult to apply statistical theory
directly to a random sample of diagrams. Instead, we can summarize the
persistent homology with the persistence landscape, introduced by Bubenik,
which converts a diagram into a well-behaved real-valued function. We
investigate the statistical properties of landscapes, such as weak convergence
of the average landscapes and convergence of the bootstrap. In addition, we
introduce an alternate functional summary of persistent homology, which we call
the silhouette, and derive an analogous statistical theory.

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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex