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Stochastic Approximate Algorithms for Uncertain Constrained K -Means Problem.
- Source :
- Mathematics (2227-7390); Jan2022, Vol. 10 Issue 1, p144, 1p
- Publication Year :
- 2022
-
Abstract
- The k-means problem has been paid much attention for many applications. In this paper, we define the uncertain constrained k-means problem and propose a (1 + ϵ) -approximate algorithm for the problem. First, a general mathematical model of the uncertain constrained k-means problem is proposed. Second, the random sampling properties of the uncertain constrained k-means problem are studied. This paper mainly studies the gap between the center of random sampling and the real center, which should be controlled within a given range with a large probability, so as to obtain the important sampling properties to solve this kind of problem. Finally, using mathematical induction, we assume that the first j − 1 cluster centers are obtained, so we only need to solve the j-th center. The algorithm has the elapsed time O ((1891 e k ϵ 2) 8 k / ϵ n d) , and outputs a collection of size O ((1891 e k ϵ 2) 8 k / ϵ n) of candidate sets including approximation centers. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 154587174
- Full Text :
- https://doi.org/10.3390/math10010144