Geodesic
Chain development
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 317-322.

Voir la notice de l'article provenant de la source Math-Net.Ru

In a finite set $X$ with distance, we introduce a so-called chain distance. This distance generates a partition of $X$ into clusters such that any point inside each cluster can be connected with any other point of the same cluster by a chain whose every link does not exceed a given threshold value. We construct a chain development, by which we mean a mapping of $X$ into a straight line that preserves the chain distance and allows one to rapidly perform clustering. We also present an efficient algorithm for constructing a chain development. 
@article{TM_2015_290_a25,
     author = {Yu. V. Malykhin and E. V. Shchepin},
     title = {Chain development},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {317--322},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a25/}
}
TY  - JOUR
AU  - Yu. V. Malykhin
AU  - E. V. Shchepin
TI  - Chain development
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2015
SP  - 317
EP  - 322
VL  - 290
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2015_290_a25/
LA  - ru
ID  - TM_2015_290_a25
ER  - 
%0 Journal Article
%A Yu. V. Malykhin
%A E. V. Shchepin
%T Chain development
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2015
%P 317-322
%V 290
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2015_290_a25/
%G ru
%F TM_2015_290_a25
Yu. V. Malykhin; E. V. Shchepin. Chain development. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 317-322. http://geodesic.mathdoc.fr/item/TM_2015_290_a25/

[1] Lemin A.Yu., “Izometrichnoe vlozhenie ravnobedrennykh (nearkhimedovykh) prostranstv v evklidovy”, DAN SSSR, 285:3 (1985), 558–562 | MR | Zbl

[2] Prim R.C., “Shortest connection networks and some generalizations”, Bell Syst. Tech. J., 36 (1957), 1389–1401 | DOI

[3] Klyahzkin V., Shchepin E., Zingerman K., “Application of hierarchical methods of cluster analysis to the printed text structure recognition”, Shape, structure and pattern recognition (Nahariya (Israel), October 4–6, 1994), World Scientific, Singapore, 1995, 333–342

[4] Klyatskin V.M., Shchepin E.V., Zingerman K.M., “Hierarchical analysis of multicolumn texts”, Pattern Recognit. Image Anal., 5:1 (1995), 87–98

[5] Kotovich N.V., “Algoritmy klasterizatsii obrazov simvolov”, Tr. ISA RAN, 38 (2008), 241–251