Minimal unimodal decomposition on trees

Yuliy Baryshnikov; Robert Ghrist

doi:10.1007/s41468-019-00046-7

Minimal unimodal decomposition on trees

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Abstract

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.

Original language	English (US)
Pages (from-to)	199-209
Number of pages	11
Journal	Journal of Applied and Computational Topology
Volume	4
Issue number	2
DOIs	https://doi.org/10.1007/s41468-019-00046-7
State	Published - Jun 2020

Keywords

Unimodal decomposition
Unimodal category
Topological data analysis

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Geometry and Topology

Online availability

10.1007/s41468-019-00046-7

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title = "Minimal unimodal decomposition on trees",

abstract = "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.",

keywords = "Unimodal decomposition, Unimodal category, Topological data analysis",

author = "Yuliy Baryshnikov and Robert Ghrist",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

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AU - Ghrist, Robert

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PY - 2020/6

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N2 - 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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KW - Unimodal decomposition

KW - Unimodal category

KW - Topological data analysis

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IS - 2

ER -

Minimal unimodal decomposition on trees

Abstract

Keywords

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Online availability

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