scholarly journals CLUSTERING AND INDEXING HISTORIC VESSEL MOVEMENT DATA WITH SPACE FILLING CURVES

2018 ◽  
Vol XLII-4 ◽  
pp. 417-424 ◽  
Author(s):  
M. Meijers ◽  
P. van Oosterom
Keyword(s):  
Integrated Approach ◽  
Space Time ◽  
Database Management System ◽  
Identification System ◽  
Time Interval ◽  
Storage Space ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Integrated Index

<p><strong>Abstract.</strong> This paper reports on the result of an on-going study using Space Filling Curves (SFCs) for indexing and clustering vessel movement message data (obtained via the Automated Identification System, AIS) inside a geographical Database Management System (Geo-DBMS). With AIS, vessels transmit their positions in intervals ranging from 2 seconds to 3 minutes. Every 6 minutes voyage related information is broadcast.</p><p> Relevant AIS messages contain a position, timestamp and vessel identifier. This information can be stored in a DBMS as separate columns with different types (as 2D point plus time plus identifier), or in an integrated column (as higher dimensional 4D point which is encoded as the position on a space filling curve, that we will call the SFC-key). Subsequently, indexing based on this SFC-key column can replace separate indexes (where this one integrated index will need less storage space than separate indexes). Moreover, this integrated index allows a good clustering (physical ordering of the table). Also, in an approach with separate indexes for location, time and object identifier the query optimizer inside a DBMS has to estimate which index is most selective for a given query. It is not possible to use two indexes at the same time &amp;ndash; e.g. in case of a space-time query. An approach with one multi-dimensional integrated index does not have this problem. It results in faster query responses when specifying multiple selection criteria; i.e. both search geometry and time interval.</p><p> We explain the steps needed to make this SFC approach available <i>fully inside</i> a DBMS (to avoid expensive data transfer to external programs during use). The SFC approach makes it possible to better cluster the (spatio-temporal) data compared to an approach with separate indexes. Moreover, we show experiments (with 723,853,597 AIS position report messages spanning 3 months, Sep&amp;ndash;Dec 2016, using data for Europe, both on-sea and inland water ways) to compare an approach based on one multi-dimensional integrated index (using a SFC) with non-integrated approach. We analyze loading time (including SFC encoding) and storage requirements, together with the speed of execution of queries and granularity of answers.</p><p> Conclusion is that time spend on query execution in case of space-time queries where both dimensions are selective using the integrated SFC approach outperforms the non-integrated approach (typically a factor 2&amp;ndash;6). Also, the SFC approach saves considerably on storage space (less space needed for indexes). Lastly, we propose some future improvements to get some better query performance using the SFC approach (e.g. IOT, range-glueing and nD-histogram).</p>

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.

Follow your curiosity, along a space-filling curve

2020 ◽  
pp. 265-272
Author(s):  
Susan D'Agostino
Keyword(s):  
Mathematics Students ◽  
German Mathematician ◽  
Space Filling ◽  
Space Filling Curve ◽  
Isaac Newton ◽  
Space Filling Curves ◽  
Filling Curve

“Follow your curiosity, along a space-filling curve” tells the story of Italian mathematician Giuseppe Peano’s quest for and discovery of a space-filling curve—a curve that completely fills a space such as a square—that most mathematicians and scientists at the time did not believe existed. For example, Isaac Newton, in his Philosophiae Naturalis Principia Mathematica, tried to ban space-filling curves. The discussion of space-filling curves is enhanced with numerous hand-drawn sketches showing how to construct German mathematician David Hilbert’s space-filling curve. Mathematics students and enthusiasts are encouraged to foster a Peano-like curiosity in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

scholarly journals Multiplicativity of the uniform norm and independent functions

1990 ◽  
Vol 42 (1) ◽  
pp. 153-155
Author(s):  
A. Guyan Robertson
Keyword(s):  
Recent Work ◽  
Lebesgue Measure ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Space Filling ◽  
Stochastic Independence ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Independent Functions ◽  
Filling Curve

It has long been known that there is a close connection between stochastic independence of continuous functions on an interval and space-filling curves [9]. In fact any two nonconstant continuous functions on [0, 1] which are independent relative to Lebesgue measure are the coordinate functions of a space filling curve. (The results of Steinhaus [9] have apparently been overlooked in more recent work in this area [3, 5, 6].)

scholarly journals A Matrix Iterative Approach to Systematically Generate Hilbert-type Space-filling Curves

2015 ◽  
Vol 14 (12) ◽  
pp. 6281-6294
Author(s):  
Ruisong Ye ◽  
Li Liu
Keyword(s):  
Point Of View ◽  
Iterative Approach ◽  
Matrix Approach ◽  
Space Filling ◽  
Type Space ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
The Matrix ◽  
Filling Curve ◽  
Hilbert Type

Hilbert-type space-filling curve has attracted much interest thanks to its mathematical importance and extensive applications in signal processing. In this paper, we construct the complete six Hilbert-type space-filling curves form amatrix point of view. The address matrix for each considered Hilbert-type space-filling curve can be easily generated by a recursive manner. Besides the six Hilbert-type space-filling curves, we also construct their corresponding variation versions. The merit of the matrix approach is that the iterative algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.

scholarly journals Deterministic Sampling from Uniform Distributions with Sierpinski Space-Filling Curves

2020 ◽  
Author(s):  
Hime Aguiar e O. Jr
Keyword(s):  
Probability Distributions ◽  
Real Interval ◽  
Space Filling ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
Uniform Distributions ◽  
Deterministic Sampling ◽  
Discrete Manner ◽  
Filling Curve ◽  
Computational Properties

In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves (SFCs), a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarilly injective, the investigation focused upon the structure of the distributions obtained when their domain is swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1], and the Sierpinski space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback-Leibler distance is used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random.

Dualism loop and string

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Space Time ◽  
Time Interval

the holographic space-time interval leads to the concept of dualism between loops and strings.

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

Tail asymptotics of an infinitely divisible space-time model with convolution equivalent Lévy measure

2021 ◽  
Vol 58 (1) ◽  
pp. 42-67 ◽  
Author(s):  
Mads Stehr ◽  
Anders Rønn-Nielsen
Keyword(s):  
Space Time ◽  
Time Interval ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Time Model ◽  
Spatial Object ◽  
Tail Behaviour ◽  
Fixed Radius ◽  
The Right ◽  
Space Time Model

AbstractWe consider a space-time random field on ${{\mathbb{R}^d} \times {\mathbb{R}}}$ given as an integral of a kernel function with respect to a Lévy basis with a convolution equivalent Lévy measure. The field obeys causality in time and is thereby not continuous along the time axis. For a large class of such random fields we study the tail behaviour of certain functionals of the field. It turns out that the tail is asymptotically equivalent to the right tail of the underlying Lévy measure. Particular examples are the asymptotic probability that there is a time point and a rotation of a spatial object with fixed radius, in which the field exceeds the level x, and that there is a time interval and a rotation of a spatial object with fixed radius, in which the average of the field exceeds the level x.

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