IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v34y2017i2d10.1007_s00357-017-9230-1.html
   My bibliography  Save this article

Robinsonian Matrices: Recognition Challenges

Author

Listed:
  • D. Fortin

    (INRIA)

Abstract

Ultrametric inequality is involved in different operations on (dis)similarity matrices. Its coupling with a compatible ordering leads to nice interpretations in seriation problems. We accurately review the interval graph recognition problem for its tight connection with recognizing a dense Robinsonian dissimilarity (precisely, in the anti-ultrametric case). Since real life matrices are prone to errors or missing entries, we address the sparse case and make progress towards recognizing sparse Robinsonian dissimilarities with lexicographic breadth first search. The ultrametric inequality is considered from the same graph point of view and the intimate connection between cocomparability graph and dense Robinsonian similarity is established. The current trend in recognizing special graph structures is examined in regard to multiple lexicographic search sweeps. Teaching examples illustrate the issues addressed for both dense and sparse symmetric matrices.

Suggested Citation

  • D. Fortin, 2017. "Robinsonian Matrices: Recognition Challenges," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 191-222, July.
    • Handle: RePEc:spr:jclass:v:34:y:2017:i:2:d:10.1007_s00357-017-9230-1
    DOI: 10.1007/s00357-017-9230-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-017-9230-1
    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/s00357-017-9230-1?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. Victor Chepoi & Bernard Fichet & Morgan Seston, 2009. "Seriation in the Presence of Errors: NP-Hardness of l ∞ -Fitting Robinson Structures to Dissimilarity Matrices," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 279-296, December.
    2. Pascal Préa & Dominique Fortin, 2014. "An Optimal Algorithm To Recognize Robinsonian Dissimilarities," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 351-385, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. D. Fortin, 2020. "Clustering Analysis of a Dissimilarity: a Review of Algebraic and Geometric Representation," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 180-202, April.
    2. Julio Aracena & Christopher Thraves Caro, 2023. "The weighted sitting closer to friends than enemies problem in the line," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.

    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. Julio Aracena & Christopher Thraves Caro, 2023. "The weighted sitting closer to friends than enemies problem in the line," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.
    2. Laurent, Monique & Seminaroti, Matteo, 2016. "Similarity-First Search : A New Algorithm With Application to Robinsonian Matrix Recognition," Other publications TiSEM 8468be57-ed46-400c-9c0e-7, Tilburg University, School of Economics and Management.
    3. Smeulders, B., 2018. "Testing a mixture model of single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 101-113.
    4. Pascal Préa & Dominique Fortin, 2014. "An Optimal Algorithm To Recognize Robinsonian Dissimilarities," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 351-385, October.
    5. Laurent, Monique & Seminaroti, M. & Tanigawa, Shin-ichi, 2017. "A structural characterization for certifying robinsonian matrices," Other publications TiSEM 5ecebfb8-804e-4267-8c12-b, Tilburg University, School of Economics and Management.

    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:jclass:v:34:y:2017:i:2:d:10.1007_s00357-017-9230-1. 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.