Space-Filling in High-Dimensional Sets

2021 ◽  
pp. 1-39
Author(s):  
Anatoly Zhigljavsky ◽  
Antanas Žilinskas
Keyword(s):  
High Dimensional ◽  
Space Filling

Construction of space-filling designs using WSP algorithm for high dimensional spaces

2012 ◽  
Vol 113 ◽  
pp. 26-31 ◽  
Author(s):  
J. Santiago ◽  
M. Claeys-Bruno ◽  
M. Sergent
Keyword(s):  
High Dimensional ◽  
Space Filling

On the Behaviour of p-Adic Scaled Space Filling Curve Indices for High-Dimensional Data

2020 ◽  
Author(s):  
Patrick Erik Bradley ◽  
Markus Wilhelm Jahn
Keyword(s):  
Gray Code ◽  
High Dimensional ◽  
Affine Transformations ◽  
Hilbert Curve ◽  
Space Filling ◽  
Real World Data ◽  
Space Filling Curve ◽  
Indexing Method ◽  
Filling Curve ◽  
Hilbert Curves

Abstract Space filling curves are widely used in computer science. In particular, Hilbert curves and their generalizations to higher dimension are used as an indexing method because of their nice locality properties. This article generalizes this concept to the systematic construction of $p$-adic versions of Hilbert curves based on special affine transformations of the $p$-adic Gray code and develops a scaled indexing method for data taken from high-dimensional spaces based on these new curves, which with increasing dimension is shown to be less space consuming than the optimal standard static Hilbert curve index. A measure is derived, which allows to assess the local sparsity of a dataset, and is tested on some real-world data.

Irregularity in high-dimensional space-filling curves

2010 ◽  
Vol 29 (3) ◽  
pp. 217-238 ◽  
Author(s):  
Mohamed F. Mokbel ◽  
Walid G. Aref
Keyword(s):  
Dimensional Space ◽  
High Dimensional ◽  
Space Filling ◽  
High Dimensional Space ◽  
Space Filling Curves

High-Dimensional Probability

2018 ◽  
Author(s):  
Roman Vershynin
Keyword(s):  
High Dimensional

The Semantic Credentials of High-Dimensional Memory Models

2014 ◽  
Author(s):  
Curt Burgess ◽  
Sarah Maples
Keyword(s):  
Memory Models ◽  
High Dimensional
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