Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Same But Different: Distance Correlations Between Topological Summaries   Persistent homology allows us to create topological summaries of complex
data. In order to analyse these statistically, we need to choose a topological
summary and a relevant metric space in which this topological summary exists.
While different summaries may contain the same information (as they come from
the same persistence module), they can lead to different statistical
conclusions since they lie in different metric spaces. The best choice of
metric will often be application-specific. In this paper we discuss distance
correlation, which is a non-parametric tool for comparing data sets that can
lie in completely different metric spaces. In particular we calculate the
distance correlation between different choices of topological summaries. We
compare some different topological summaries for a variety of random models of
underlying data via the distance correlation between the samples. We also give
examples of performing distance correlation between topological summaries and
other scalar measures of interest, such as a paired random variable or a
parameter of the random model used to generate the underlying data. This
article is meant to be expository in style, and will include the definitions of
standard statistical quantities in order to be accessible to non-statisticians.

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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: hep-ex