Zobrazeno 1 - 10
of 104
pro vyhledávání: '"Alexander Kel'manov"'
Publikováno v:
Annals of Mathematics and Artificial Intelligence. 90:965-977
In this paper we consider two closely related problems of selecting a diverse subset of points with respect to squared Euclidean distance. Given a set of points in Euclidean space, the first problem is to find a subset of a specified size M maximizin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::923c001996d58820b56327a1ebe8b7b9
https://doi.org/10.1007/s10472-021-09773-z
https://doi.org/10.1007/s10472-021-09773-z
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 313:S117-S124
We consider the problem of partitioning a set of $$N$$ points in $$d$$ -dimensional Euclidean space into two clusters minimizing the sum of the squared distances between each element and the center of the cluster to which it belongs. The center of th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::feb72d251a424806518ff7a800356176
https://doi.org/10.1134/s0081543821030123
https://doi.org/10.1134/s0081543821030123
Publikováno v:
Computational Mathematics and Mathematical Physics. 61:1153-1161
A previously unstudied optimization problem induced by noise-proof recognition of a quasi-periodic sequence, namely, by the recognition of a sequence $$Y$$ of length $$N$$ generated by a sequence $$U$$ belonging to a given finite set $$W$$ (alphabet)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::038291746517284631b4f9a4bace3f2c
https://doi.org/10.1134/s0965542521070095
https://doi.org/10.1134/s0965542521070095
Publikováno v:
Computational Mathematics and Mathematical Physics. 60:1951-1963
A previously unstudied optimization problem concerning the summation of elements of numerical sequences $$Y$$ and $$U$$ of respective lengths $$N$$ and $$q \leqslant N$$ is considered. The task is to minimize the sum of differences between weighted c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c6315ae07c725730d31cc4a11d29d360
https://doi.org/10.1134/s0965542520120052
https://doi.org/10.1134/s0965542520120052
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 309:S65-S73
Two similar problems of searching for a family of disjoint subsets (clusters) in a finite set of points in Euclidean space are considered. In these problems, the size of the smallest cluster should be maximized so that in each cluster the intracluste
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3cb47849522b355dc8f1bb12baff13f2
https://doi.org/10.1134/s0081543820040082
https://doi.org/10.1134/s0081543820040082
Publikováno v:
Numerical Analysis and Applications. 13:103-116
We consider an unstudied optimization problem of summing elements of two numerical sequences: $$Y$$ of length $$N$$ and $$U$$ of length $$q\leq N$$ . The objective of the problem is minimization of the sum of differences of weighted convolutions of s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a4d14dc68bc5f5dc304fd78f245a9974
https://doi.org/10.1134/s1995423920020020
https://doi.org/10.1134/s1995423920020020
Publikováno v:
Computational Mathematics and Mathematical Physics. 60:163-170
We consider three related problems of partitioning an N-element set of points in d-dimensional Euclidean space into two clusters balancing the value of the intracluster quadratic variance normalized by the cluster size in the first problem, the intra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5e4c30cb7fef20f8ef0e4cc5ebd2750c
https://doi.org/10.1134/s096554251911006x
https://doi.org/10.1134/s096554251911006x
Publikováno v:
Доклады Академии наук. 489:339-343
We consider the problem of clustering a finite set of N points in d-dimensional Euclidean space into two clusters minimizing the sum (over both clusters) of the intracluster sums of the squared distances between the cluster elements and their centers
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2c495eb3892c9e611f70e15209b22148
https://doi.org/10.31857/s0869-56524894339-343
https://doi.org/10.31857/s0869-56524894339-343
Autor:
Alexander Kel'manov, P. S. Ruzankin
Publikováno v:
Pattern Recognition and Image Analysis. 29:573-576
The known quadratic $$NP$$-hard (in the strong sense) $$M$$-variance problem is considered. It arises in the following typical problem of data analysis: in a set of $$N$$ objects determined by their characteristics (features), find a subset of $$M$$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::57ec789d3055e5a7155adf4f85de675d
https://doi.org/10.1134/s1054661819040072
https://doi.org/10.1134/s1054661819040072
Publikováno v:
Доклады Академии наук. 488:16-20
We consider some problems of partitioning a finite set of N points in d-dimension Euclidean space into two clusters balancing the value of (1) the quadratic variance normalized by a cluster size, (2) the quadratic variance, and (3) the size-weighted
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fd4783a91d738f30e63029bb47ec5e93
https://doi.org/10.31857/s0869-5652488116-20
https://doi.org/10.31857/s0869-5652488116-20