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Minimal unimodal decomposition on trees


The decomposition of a density function on a domain into a minimal sum of unimodal components is a fundamental problem in statistics, leading to the topological invariant of unimodal category of a density. This paper gives an efficient algorithm for the construction of a minimal unimodal decomposition of a tame density function on a finite metric tree.

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This research was done while YB was visiting the Departments of Mathematics and ESE of the University of Pennsylvania—the hospitality of both departments is warmly appreciated.

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Correspondence to Yuliy Baryshnikov.

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Work supported by the National Science Foundation via DMS-1622370. Work supported by the Office of the Assistant Secretary of Defense Research and Engineering through ONR N00014-16-1-2010.

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Baryshnikov, Y., Ghrist, R. Minimal unimodal decomposition on trees. J Appl. and Comput. Topology 4, 199–209 (2020).

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  • Unimodal decomposition
  • Unimodal category
  • Topological data analysis

Mathematics Subject Classification

  • 58E05
  • 62G08