Definition
Let P = {p1, p2, …} be a stream of points in the metric space (X, Lq). Usually, X = ℝd or X = {1, … , U}d (discrete case), and Lq = L2 is the Euclidean distance. The set P is called a spatial data stream. Geometric stream mining algorithms compute the (approximate) answer to a geometric question over the subset of P seen so far. For example, the diameter problem asks to maintain the pair of points that are farthest away in the current stream. A more comprehensive list of problems is presented later.
Historical Background
Geometric algorithms in the offline setting have been extensively studied over the past decades. Their applications encompass many fields, such as image processing, robotics, data mining, or VLSI design. For an introduction to computational geometry, refer to the book [8]. On the other hand, research on spatial data streams is a recent development. Shortly after the first results on numeric data streams appeared, a slew of papers argued that in many...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Recommended Reading
Agarwal PK, Har-Peled S, Varadarajan KR. Approximating extent measures of points. J ACM. 2004;51(4):606–33.
Bagchi A, Chaudhary A, Eppstein D, Goodrich MT. Deterministic sampling and range counting in geometric data streams. In: Proceedings of the 20th Annual Symposium on Computational Geometry; 2004.p. 144–51.
Chan TM. Faster core-set constructions and data-stream algorithms in fixed dimensions. Comput Geom. 2006;35(1–2):20–35.
Cormode G, Muthukrishnan S, Rozenbaum I Summarizing and mining inverse distributions on data streams via dynamic inverse sampling. In: Proceedings of the 31st International Conference on Very Large Data Bases; 2005. p. 25–36.
Frahling G, Indyk P, Sohler C Sampling in dynamic data streams and applications. In: Proceedings of the 21st Annual Symposium on Computational Geometry; 2005. 142–9.
Indyk P. Algorithms for dynamic geometric problems over data streams. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing; 2004. p. 373–80.
Korn F, Muthukrishnan S, Srivastava D. Reverse nearest neighbor aggregates over data streams. In: Proceedings of the 28th International Conference on Very Large Data Bases; 2002. p. 814–25.
Preparata FP, Shamos MI. Computational geometry: an introduction. 3rd ed. Berlin/Hiedelberg/New York: Springer; 1990.
Vitter JS. Random sampling with a reservoir. ACM Trans Math Software. 1985;11(1):37–57.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media, LLC, part of Springer Nature
About this entry
Cite this entry
Procopiuc, C.M. (2018). Geometric Stream Mining. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_180
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8265-9_180
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8266-6
Online ISBN: 978-1-4614-8265-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering