Probabilistic analysis of vantage point trees

Probabilistic properties of vantage point trees are studied. A vp-tree built from a sequence of independent identically distributed points in ${[-1,\hspace{0.1667em}1]^{d}}$ with the ${\ell _{\infty }}$-distance function is considered. The length of the leftmost path in the tree, as well as partitio...

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Autor principal:	Vladyslav Bohun
Formato:	article
Lenguaje:	EN
Publicado:	VTeX 2021
Materias:	Fixed-point equation machine learning Markov chain nearest neighbor search probabilistic analysis random tree Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d9dfff7dfd874d459844ae2798bdc000
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spelling	oai:doaj.org-article:d9dfff7dfd874d459844ae2798bdc0002021-11-17T08:47:29ZProbabilistic analysis of vantage point trees10.15559/21-VMSTA1882351-60462351-6054https://doaj.org/article/d9dfff7dfd874d459844ae2798bdc0002021-08-01T00:00:00Zhttps://www.vmsta.org/doi/10.15559/21-VMSTA188https://doaj.org/toc/2351-6046https://doaj.org/toc/2351-6054Probabilistic properties of vantage point trees are studied. A vp-tree built from a sequence of independent identically distributed points in ${[-1,\hspace{0.1667em}1]^{d}}$ with the ${\ell _{\infty }}$-distance function is considered. The length of the leftmost path in the tree, as well as partitions over the space it produces are analyzed. The results include several convergence theorems regarding these characteristics, as the number of nodes in the tree tends to infinity.Vladyslav BohunVTeXarticleFixed-point equationmachine learningMarkov chainnearest neighbor searchprobabilistic analysisrandom treeApplied mathematics. Quantitative methodsT57-57.97MathematicsQA1-939ENModern Stochastics: Theory and Applications, Vol 8, Iss 4, Pp 413-434 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Fixed-point equation machine learning Markov chain nearest neighbor search probabilistic analysis random tree Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
spellingShingle	Fixed-point equation machine learning Markov chain nearest neighbor search probabilistic analysis random tree Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939 Vladyslav Bohun Probabilistic analysis of vantage point trees
description	Probabilistic properties of vantage point trees are studied. A vp-tree built from a sequence of independent identically distributed points in ${[-1,\hspace{0.1667em}1]^{d}}$ with the ${\ell _{\infty }}$-distance function is considered. The length of the leftmost path in the tree, as well as partitions over the space it produces are analyzed. The results include several convergence theorems regarding these characteristics, as the number of nodes in the tree tends to infinity.
format	article
author	Vladyslav Bohun
author_facet	Vladyslav Bohun
author_sort	Vladyslav Bohun
title	Probabilistic analysis of vantage point trees
title_short	Probabilistic analysis of vantage point trees
title_full	Probabilistic analysis of vantage point trees
title_fullStr	Probabilistic analysis of vantage point trees
title_full_unstemmed	Probabilistic analysis of vantage point trees
title_sort	probabilistic analysis of vantage point trees
publisher	VTeX
publishDate	2021
url	https://doaj.org/article/d9dfff7dfd874d459844ae2798bdc000
work_keys_str_mv	AT vladyslavbohun probabilisticanalysisofvantagepointtrees
_version_	1718425704469626880

Probabilistic analysis of vantage point trees

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