Abstract
It is shown that the complete linkage clustering of a set of n points in ād where d ā„ 1 is a constant, can be computed in optimal O(n log n) time and linear space, under the L 1 and Lā-metric. Furthermore, it is shown that, for every other fixed L t -metric, it can be approximated within an arbitrarily small constant factor in O(n log n) time using linear space.
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References
P. Arabie, L. J. Hubert, and G. De Soete, editors. Clustering and Classification. World Scientific, 1996.
F. Aurenhammer and R. Klein. Voronoi diagrams. Technical Report 198-5, Informatik, FernUniversitƤt, Hagen, Germany, 1996.
S. N. Bespamyatnikh. An optimal algorithm for closest pair maintenance. In Proceedings of the 11th Annual ACM Symposium on Computational Geometry, pages 152ā161, 1995.
W. H. E. Day and H. Edelsbrunner. Efficient algorithms for agglomerative hierarchical clustering methods. Journal of Classification, 1(1):7ā24, 1984.
D. Defays. An efficient algorithm for a complete link method. Computer Journal, 20:364ā366, 1977.
J. C. Gower. A comparison of some methods of cluster analysis. Biometrics, 23:623ā638, 1967.
D. Krznaric and C. Levcopoulos. The first subquadratic algorithm for complete linkage clustering. In Proceedings of ISAAC '95, LNCS 1004, pages 392ā401. Springer, 1995.
T. Kurita. An efficient agglomerative clustering algorithm using a heap. Pattern Recognition, 24(3):205ā209, 1991.
KÅivĆ”nek. Connected admissible hierarchical clustering. Paper presented at the DIANA III conference, Bechyne, Czechoslovakia, June 1990.
G. N. Lance and W. T. Williams. A generalised sorting strategy for computer classifications. Nature, 212:218, 1966.
X. Li. Parallel algorithms for hierarchical clustering and cluster validity. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(11):1088ā1092, 1990.
F. Murtagh. Complexities of hierarchic clustering algorithms: State of the art. Computational Statistics Quarterly, 1:101ā113, 1984.
F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York, 1985.
R. R. Sokal and C. D. Michener. A statistical method for evaluating systematic relationships. University of Kansas Science Bulletin, 38:1409ā1438, 1958.
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Krznaric, D., Levcopoulos, C. (1997). Optimal algorithms for complete linkage clustering in d dimensions. In: PrĆvara, I., RužiÄka, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029980
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DOI: https://doi.org/10.1007/BFb0029980
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