IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v37y2019i4d10.1007_s10878-018-0354-y.html
   My bibliography  Save this article

LP-based pivoting algorithm for higher-order correlation clustering

Author

Listed:
  • Takuro Fukunaga

    (RIKEN Center for Advanced Intelligence Project)

Abstract

Correlation clustering is an approach for clustering a set of objects from given pairwise information. In this approach, the given pairwise information is usually represented by an undirected graph with nodes corresponding to the objects, where each edge in the graph is assigned a nonnegative weight, and either the positive or negative label. Then, a clustering is obtained by solving an optimization problem of finding a partition of the node set that minimizes the disagreement or maximizes the agreement with the pairwise information. In this paper, we extend correlation clustering with disagreement minimization to deal with higher-order relationships represented by hypergraphs. We give two pivoting algorithms based on a linear programming relaxation of the problem. One achieves an $$O(k \log n)$$ O ( k log n ) -approximation, where n is the number of nodes and k is the maximum size of hyperedges with the negative labels. This algorithm can be applied to any hyperedges with arbitrary weights. The other is an O(r)-approximation for complete r-partite hypergraphs with uniform weights. This type of hypergraphs arise from the coclustering setting of correlation clustering.

Suggested Citation

  • Takuro Fukunaga, 2019. "LP-based pivoting algorithm for higher-order correlation clustering," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1312-1326, May.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:4:d:10.1007_s10878-018-0354-y
    DOI: 10.1007/s10878-018-0354-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0354-y
    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/s10878-018-0354-y?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dewan F. Wahid & Elkafi Hassini, 2022. "A Literature Review on Correlation Clustering: Cross-disciplinary Taxonomy with Bibliometric Analysis," SN Operations Research Forum, Springer, vol. 3(3), pages 1-42, September.
    2. Sai Ji & Yinhong Dong & Donglei Du & Dongzhao Wang & Dachuan Xu, 2023. "Approximation algorithms for the lower bounded correlation clustering problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-19, January.

    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:37:y:2019:i:4:d:10.1007_s10878-018-0354-y. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.