Exact computation of the halfspace depth

For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of n points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of these algorithms the depth is calculated as the minimum over a f...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Computational statistics & data analysis Ročník 98; s. 19 - 30
Hlavní autoři: Dyckerhoff, Rainer, Mozharovskyi, Pavlo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.06.2016
Elsevier
Témata:
Algorithms
Clouds
Combinatorial algorithm
Computation
Computer simulation
Data processing
Exact algorithm
Mathematical analysis
Orthogonal complement
Projection
Statistics
Tukey depth
Orthogonal complement
Projection
Tukey depth
Exact algorithm
Combinatorial algorithm
ISSN:0167-9473, 1872-7352
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of n points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of these algorithms the depth is calculated as the minimum over a finite number of depth values w.r.t. proper projections of the data cloud. Three variants of this class are studied in more detail. All of these algorithms are capable of dealing with data that are not in general position and even with data that contain ties. As is shown by simulations, all proposed algorithms prove to be very efficient.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2015.12.011