On the Behaviour of p-Adic Scaled Space Filling Curve Indices for High-Dimensional Data. (13th July 2020)

• Record Type: Journal Article
• Authors: Bradley, Patrick Erik; Jahn, Markus Wilhelm
• Is Part Of: Computer journal. Volume 65:Number 2(2022)
• Page Start: 310
• Page End: 330
• Publication Date: 2020-07-13
• Subjects: Gray code -- Hilbert curve -- index -- scalability -- high dimension -- p-adic number; Computers -- Periodicals; 005.1
• DOI: 10.1093/comjnl/bxaa036
• Languages: English
• ISSNs: 0010-4620

Abstract

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.