Geodesic
On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 1, pp. 170-179 
A. S. Val'kov. On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 1, pp. 170-179. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_1_a11/
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     title = {On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The concept of a hierarchical $\varepsilon$-cluster structure is defined, and the properties of such structures are studied. The uniqueness of the decomposition of a metric configuration into a hierarchy of $\varepsilon$ clusters is proved for $\varepsilon<1$. The problem of finding a hierarchical $\varepsilon$-cluster structure in a metric configuration is studied. In the general case, the complexity of this problem is $O(N^2)$. An algorithm for solving this problem is proposed that has complexity from $O(N\ln N)$ to $O(N^2)$ on some specific classes of metric configurations.

[1] Zhuravlev Yu. I., “Korrektnye algebry nad mnozhestvami nekorrektnykh (evristicheskikh) algoritmov, I”, Kibernetika, 1977, no. 4, 5–17

[2] Aizerman M. A., Braverman E. M., Rozonoer L. I., Metod potentsialnykh funktsii v teorii obucheniya mashin, Nauka, M., 1970

[3] Maneewongvatana S., Mount D. M., “Analysis of approximate nearest neighbor searching with clustered point sets”, ALENEX 99, 1999

[4] Volmer S., “Fast approximate nearest-neighbor queries in metric feature spaces by buoy indexing”, Proc. 5th Internat. Conf. on Visual Inform. Systems (Hsin Chu, Taiwan, 2002), 36–49 | Zbl