Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem

Lu, Jianguang; Tang, Juan; Xing, Bin; Tang, Xianghong

doi:10.3390/math10010144

Open AccessArticle

Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem

¹

State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China

²

Chongqing Innovation Center of Industrial Big-Data Co., Ltd., Chongqing 400707, China

³

School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China

⁴

Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China

⁵

National Engineering Laboratory for Industrial Big-Data Application Technology, Chongqing 400707, China

^*

Author to whom correspondence should be addressed.

Mathematics 2022, 10(1), 144; https://doi.org/10.3390/math10010144

Submission received: 25 November 2021 / Revised: 24 December 2021 / Accepted: 27 December 2021 / Published: 4 January 2022

(This article belongs to the Special Issue Advanced Mathematical Methods in Intelligent Multimedia: Security and Applications)

Download

Browse Figure

Versions Notes

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 ({(\frac{1891 e k}{ϵ^{2}})}^{8 k / ϵ} n d)

, and outputs a collection of size

O ({(\frac{1891 e k}{ϵ^{2}})}^{8 k / ϵ} n)

of candidate sets including approximation centers.

Keywords: stochastic approximate algorithms; uncertain constrained k-means; approximation centers

Share and Cite

MDPI and ACS Style

Lu, J.; Tang, J.; Xing, B.; Tang, X. Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem. Mathematics 2022, 10, 144. https://doi.org/10.3390/math10010144

AMA Style

Lu J, Tang J, Xing B, Tang X. Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem. Mathematics. 2022; 10(1):144. https://doi.org/10.3390/math10010144

Chicago/Turabian Style

Lu, Jianguang, Juan Tang, Bin Xing, and Xianghong Tang. 2022. "Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem" Mathematics 10, no. 1: 144. https://doi.org/10.3390/math10010144

APA Style

Lu, J., Tang, J., Xing, B., & Tang, X. (2022). Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem. Mathematics, 10(1), 144. https://doi.org/10.3390/math10010144

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Stochastic Approximate Algorithms for Uncertain Constrained K-Means Problem

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI