Minimal Unimodal Decompositions on Trees
Yuliy Baryshnikov, Robert Ghrist

TL;DR
This paper introduces an efficient algorithm for decomposing a density function on a finite metric tree into a minimal sum of unimodal components, advancing the understanding of unimodal categories in topological data analysis.
Contribution
It provides the first efficient algorithm for minimal unimodal decomposition of tame density functions on finite metric trees, a key problem in topological statistics.
Findings
Algorithm successfully computes minimal unimodal decompositions
Improves computational efficiency over previous methods
Enhances topological analysis of density functions 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.
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Taxonomy
TopicsData Management and Algorithms · Bayesian Methods and Mixture Models · Topological and Geometric Data Analysis
