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...

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Veröffentlicht in:Computational statistics & data analysis Jg. 98; S. 19 - 30
Hauptverfasser: Dyckerhoff, Rainer, Mozharovskyi, Pavlo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.06.2016
Elsevier
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie: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