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Author:

Ren, Chunying (Ren, Chunying.) | Xu, Dachuan (Xu, Dachuan.) | Du, Donglei (Du, Donglei.) | Li, Min (Li, Min.)

Indexed by:

CPCI-S EI Scopus

Abstract:

In the classical k-means problem, we are given a data set D subset of R-l and an integer k. The object is to select a set S subset of R-l of size at most k such that each point in D is connected to the closet cluster in S with minimum total squared distances. However, in some real-life applications, it is more desirable and beneficial to pay a small penalty for not connecting some outliers in D that are too far away from most points. As a result, we are motivated to study the k-means problem with penalties, for which we propose a (6.357+epsilon)-approximation algorithm via the primal-dual technique, improving the previous best approximation ratio of 19.849 + is an element of in [7] also by using the primal-dual technique.

Keyword:

Primal-dual Penalties k-means problem Approximation algorithm

Author Community:

  • [ 1 ] [Ren, Chunying]Beijing Univ Technol, Dept Operat Res & Informat Engn, Beijing 100124, Peoples R China
  • [ 2 ] [Xu, Dachuan]Beijing Univ Technol, Dept Operat Res & Informat Engn, Beijing 100124, Peoples R China
  • [ 3 ] [Du, Donglei]Univ New Brunswick, Fac Management, Fredericton, NB E3B 5A3, Canada
  • [ 4 ] [Li, Min]Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China

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Source :

THEORY AND APPLICATIONS OF MODELS OF COMPUTATION, TAMC 2020

ISSN: 0302-9743

Year: 2020

Volume: 12337

Page: 377-389

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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