Enclosing Depth and Other Depth Measures

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Enclosing Depth and Other Depth Measures. / Schnider, Patrick.

I: Combinatorica, Bind 43, Nr. 5, 2023, s. 1007-1029.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Schnider, P 2023, 'Enclosing Depth and Other Depth Measures', Combinatorica, bind 43, nr. 5, s. 1007-1029. https://doi.org/10.1007/s00493-023-00045-4

APA

Schnider, P. (2023). Enclosing Depth and Other Depth Measures. Combinatorica, 43(5), 1007-1029. https://doi.org/10.1007/s00493-023-00045-4

Vancouver

Schnider P. Enclosing Depth and Other Depth Measures. Combinatorica. 2023;43(5):1007-1029. https://doi.org/10.1007/s00493-023-00045-4

Author

Schnider, Patrick. / Enclosing Depth and Other Depth Measures. I: Combinatorica. 2023 ; Bind 43, Nr. 5. s. 1007-1029.

Bibtex

@article{93db90a09ad64d35a2a5b8f76c2b145d,
title = "Enclosing Depth and Other Depth Measures",
abstract = "We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the Cascade conjecture, introduced by Kalai for Tverberg depth, holds for all depth measures which satisfy our most restrictive set of axioms, which includes Tukey depth. Along the way, we introduce and study a new depth measure called enclosing depth, which we believe to be of independent interest, and show its relation to a constant-fraction Radon theorem on certain two-colored point sets.",
keywords = "Combinatorial depth measures, Discrete geometry, Topological methods",
author = "Patrick Schnider",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",
year = "2023",
doi = "10.1007/s00493-023-00045-4",
language = "English",
volume = "43",
pages = "1007--1029",
journal = "Combinatorica",
issn = "0209-9683",
publisher = "Springer",
number = "5",

}

RIS

TY - JOUR

T1 - Enclosing Depth and Other Depth Measures

AU - Schnider, Patrick

N1 - Publisher Copyright: © 2023, The Author(s).

PY - 2023

Y1 - 2023

N2 - We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the Cascade conjecture, introduced by Kalai for Tverberg depth, holds for all depth measures which satisfy our most restrictive set of axioms, which includes Tukey depth. Along the way, we introduce and study a new depth measure called enclosing depth, which we believe to be of independent interest, and show its relation to a constant-fraction Radon theorem on certain two-colored point sets.

AB - We study families of depth measures defined by natural sets of axioms. We show that any such depth measure is a constant factor approximation of Tukey depth. We further investigate the dimensions of depth regions, showing that the Cascade conjecture, introduced by Kalai for Tverberg depth, holds for all depth measures which satisfy our most restrictive set of axioms, which includes Tukey depth. Along the way, we introduce and study a new depth measure called enclosing depth, which we believe to be of independent interest, and show its relation to a constant-fraction Radon theorem on certain two-colored point sets.

KW - Combinatorial depth measures

KW - Discrete geometry

KW - Topological methods

U2 - 10.1007/s00493-023-00045-4

DO - 10.1007/s00493-023-00045-4

M3 - Journal article

AN - SCOPUS:85163127457

VL - 43

SP - 1007

EP - 1029

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 5

ER -

ID: 359597345