Abstract
This paper presents a new data structure called Voronoi tree to support the solution of proximity problems in general pseudo metric spaces with efficiently computable distance functions. We analyse some structural properties and report experimental results showing that Voronoi trees are a proper and very efficient tool for the representation of proximity properties and generation of suitable clusterings.
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References
F.Dehne: AN O(n4) Algorithm to Construct all Voronoi Diagrams for K Nearest Neighbor Searching in the Euclidean Plane, Proceedings of the 10th International Colloquium on Automata, Languages and Programming (ICALP ’83), Barcelona (Spain), July 18–22, 1983, Lecture Notes in Computer Science, No. 154, Springer 1983
F.Dehne: Optical Clustering, Report, Informatik I, Wuerzburg, 1985
Dubes,Jain: Clustering Methodologies in Exploratory Data Analysis, in M.C.Yovits (Ed.): Advances in Computers, Vol.19, Academic Press, 1980
F. Dehne, H. Noltemeier: Clustering Geometric Objects and Applications to Layout Problems, Proceedings Computer Graphics 1985, Tokyo, Springer, Tokyo 1985
F.Dehne, H.Noltemeier: A Computational Geometry Approach to Clustering Problems, Proceedings of the 1st ACM SIGGRAPH Symposium on Computational Geometry, Baltimore, MD, June 5–7, 1985
F.Dehne, H.Noltemeier: Clustering Methods for Geometric Objects and Applications to Design Problems, Report, Informatik I, Wuerzburg 1985, to appear in: IEEE Computer Graphics and Applications, special issue: Computer Graphics Tokyo 85
E. Diday, J.C. Simon, Clustering Analysis, in K.S. Fu (ed.), Digital Pattern Recognition, Springer, Berlin, Heidelberg, New York, 1980
I. Kalantari, G. McDonald: A Data structure and an Algorithm for the Nearest Point Problem, IEEE Transactions on Software Engineering, Vol. SE-9, No.5, Sept.83
H. Noltemeier: Distances in Hypergraphs, Report, Informatik I, Wuerzburg 1985
Shamos, Hoey: Closest Point Problems, Proc. 16th Ann. IEEE Symp. on Found, of Comp. Sci., 1975
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© 1988 Springer-Verlag Berlin Heidelberg
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Dehne, F., Noltemeier, H. (1988). Voronoi Trees and Clustering Problems. In: Ferraté, G., Pavlidis, T., Sanfeliu, A., Bunke, H. (eds) Syntactic and Structural Pattern Recognition. NATO ASI Series, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83462-2_12
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DOI: https://doi.org/10.1007/978-3-642-83462-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83464-6
Online ISBN: 978-3-642-83462-2
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