IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v44y2022i3d10.1007_s10878-020-00569-1.html
   My bibliography  Save this article

The seeding algorithm for spherical k-means clustering with penalties

Author

Listed:
  • Sai Ji

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Longkun Guo

    (Qilu University of Technology (Shandong Academy of Sciences))

  • Min Li

    (Shandong Normal University)

  • Dongmei Zhang

    (Shandong Jianzhu University)

Abstract

Spherical k-means clustering as a known NP-hard variant of the k-means problem has broad applications in data mining. In contrast to k-means, it aims to partition a collection of given data distributed on a spherical surface into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In the paper, we introduce spherical k-means clustering with penalties and give a $$2\max \{2,M\}(1+M)(\ln k+2)$$ 2 max { 2 , M } ( 1 + M ) ( ln k + 2 ) -approximation algorithm. Moreover, we prove that when against spherical k-means clustering with penalties but on separable instances, our algorithm is with an approximation ratio $$2\max \{3,M+1\}$$ 2 max { 3 , M + 1 } with high probability, where M is the ratio of the maximal and the minimal penalty cost of the given data set.

Suggested Citation

  • Sai Ji & Dachuan Xu & Longkun Guo & Min Li & Dongmei Zhang, 2022. "The seeding algorithm for spherical k-means clustering with penalties," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1977-1994, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00569-1
    DOI: 10.1007/s10878-020-00569-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00569-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-020-00569-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Min Li & Dachuan Xu & Jun Yue & Dongmei Zhang & Peng Zhang, 2020. "The seeding algorithm for k-means problem with penalties," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 15-32, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peihuang Huang & Pei Yao & Zhendong Hao & Huihong Peng & Longkun Guo, 2021. "Improved Constrained k -Means Algorithm for Clustering with Domain Knowledge," Mathematics, MDPI, vol. 9(19), pages 1-14, September.
    2. Xiaoyun Tian & Dachuan Xu & Donglei Du & Ling Gai, 2022. "The spherical k-means++ algorithm via local search scheme," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2375-2394, November.
    3. Min Li, 0. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.
    4. Sai Ji & Dachuan Xu & Longkun Guo & Min Li & Dongmei Zhang, 0. "The seeding algorithm for spherical k-means clustering with penalties," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-18.
    5. Min Li, 2022. "The bi-criteria seeding algorithms for two variants of k-means problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1693-1704, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00569-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.