Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Metric for Tree-Like Topological Summaries   In this work we define a novel metric structure for a family of tree-like
topological summaries. This family of objects is a natural combinatoric
generalization of merge trees of real valued functions and hierarchical
dendrograms which produces trees enriched with additional information regarding
data. The metric introduced can be computed with a dynamical integer linear
programming approach and we showcase its feasibility and the effectiveness of
the whole framework with simulated data sets. In particular we stress the
versatility of these topological summaries, which prove to be very effective in
situation where other topological data analysis tools, like persistence
diagrams, can not be meaningfully employed.

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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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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: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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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: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: physics