Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Data Analysis in Information Space   Various kinds of data are routinely represented as discrete probability
distributions. Examples include text documents summarized by histograms of word
occurrences and images represented as histograms of oriented gradients. Viewing
a discrete probability distribution as a point in the standard simplex of the
appropriate dimension, we can understand collections of such objects in
geometric and topological terms. Importantly, instead of using the standard
Euclidean distance, we look into dissimilarity measures with
information-theoretic justification, and we develop the theory needed for
applying topological data analysis in this setting. In doing so, we emphasize
constructions that enable usage of existing computational topology software in
this context.

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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph