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.

scholarly journals Tag-systems for the Hilbert curve

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Patrice Séébold
Keyword(s):  
Hilbert Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Finite Approximations ◽  
Infinite Word ◽  
International Audience ◽  
Filling Curve

International audience Hilbert words correspond to finite approximations of the Hilbert space filling curve. The Hilbert infinite word H is obtained as the limit of these words. It gives a description of the Hilbert (infinite) curve. We give a uniform tag-system to generate automatically H and, by showing that it is almost cube-free, we prove that it cannot be obtained by simply iterating a morphism.

Region of Interest Based MRI Brain Image Compression Using Peano Space Filling Curve

2016 ◽  
Vol 11 (2) ◽  
pp. 114-120 ◽  
Author(s):  
C. Peter Devadoss ◽  
Balasubramanian Sankaragomathi ◽  
Thirugnanasambantham Monica
Keyword(s):  
Image Compression ◽  
Region Of Interest ◽  
Space Filling ◽  
Brain Image ◽  
Space Filling Curve ◽  
Mri Brain ◽  
Filling Curve ◽  
Mri Brain Image

A Space Filling Curve

1983 ◽  
Vol 90 (4) ◽  
pp. 283
Author(s):  
Liu Wen
Keyword(s):  
Space Filling ◽  
Space Filling Curve ◽  
Filling Curve

scholarly journals The Effect of Space-filling Curves on the Efficiency of Hand Gesture Recognition Based on sEMG Signals

2021 ◽  
Vol 12 (1) ◽  
pp. 23-31
Author(s):  
Panagiotis Tsinganos ◽  
Bruno Cornelis ◽  
Jan Cornelis ◽  
Bart Jansen ◽  
Athanassios Skodras
Keyword(s):  
Computer Vision ◽  
Gesture Recognition ◽  
Hand Gesture Recognition ◽  
Hand Gesture ◽  
Network Architectures ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Semg Signals

Over the past few years, Deep learning (DL) has revolutionized the field of data analysis. Not only are the algorithmic paradigms changed, but also the performance in various classification and prediction tasks has been significantly improved with respect to the state-of-the-art, especially in the area of computer vision. The progress made in computer vision has produced a spillover in many other domains, such as biomedical engineering. Some recent works are directed towards surface electromyography (sEMG) based hand gesture recognition, often addressed as an image classification problem and solved using tools such as Convolutional Neural Networks (CNN). This paper extends our previous work on the application of the Hilbert space-filling curve for the generation of image representations from multi-electrode sEMG signals, by investigating how the Hilbert curve compares to the Peano- and Z-order space-filling curves. The proposed space-filling mapping methods are evaluated on a variety of network architectures and in some cases yield a classification improvement of at least 3%, when used to structure the inputs before feeding them into the original network architectures.

scholarly journals Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Ho-Kwok Dai ◽  
Hung-Chi Su
Keyword(s):  
Random Walk ◽  
Dimensional Space ◽  
Hilbert Curve ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Order Curve ◽  
Cluster Distance ◽  
The Mean ◽  
Curve Family

International audience A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.

scholarly journals Enhancing Quad Tree for Spatial Index Using Space Filling Curves

2020 ◽  
Vol 38 (1B) ◽  
pp. 15-25
Author(s):  
Ali A. Hussain ◽  
Rehab F. Hassan
Keyword(s):  
Spatial Databases ◽  
Space Filling ◽  
Space Filling Curve ◽  
Effective Implementation ◽  
Quad Tree ◽  
Implementation Time ◽  
Spatial Indexes ◽  
Space Requirements ◽  
Filling Curve ◽  
And Storage

Spatial indexes, such as those based on the Quad Tree, are important in spatial databases for the effective implementation of queries with spatial constraints, especially when queries involve spatial links. The quaternary trees are a very interesting subject, given the fact that they give the ability to solve problems in a way that focuses only on the important areas with the highest density of information. Nevertheless, it is not without the disadvantages because the search process in the quad tree suffers from the problem of repetition when reaching the terminal node and return to the behavior of another way in the search and lead to the absorption of large amounts of time and storage. In this paper, the quad tree was improved by combining it with one of the space filling curve types, resulting in reduced storage space requirements and improved implementation time

Sign in / Sign up

Export Citation Format

Share Document