IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v18y2024i1d10.1007_s11634-023-00566-2.html
   My bibliography  Save this article

A between-cluster approach for clustering skew-symmetric data

Author

Listed:
  • Donatella Vicari

    (Sapienza University of Rome)

  • Cinzia Di Nuzzo

    (Sapienza University of Rome
    University of Catania)

Abstract

In order to investigate exchanges between objects, a clustering model for skew-symmetric data is proposed, which relies on the between-cluster effects of the skew-symmetries that represent the imbalances of the observed exchanges between pairs of objects. The aim is to detect clusters of objects that share the same behaviour of exchange so that origin and destination clusters are identified. The proposed model is based on the decomposition of the skew-symmetric matrix pertaining to the imbalances between clusters into a sum of a number of off-diagonal block matrices. Each matrix can be approximated by a skew-symmetric matrix by using a truncated Singular Value Decomposition (SVD) which exploits the properties of the skew-symmetric matrices. The model is fitted in a least-squares framework and an efficient Alternating Least Squares algorithm is provided. Finally, in order to show the potentiality of the model and the features of the resulting clusters, an extensive simulation study and an illustrative application to real data are presented.

Suggested Citation

  • Donatella Vicari & Cinzia Di Nuzzo, 2024. "A between-cluster approach for clustering skew-symmetric data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(1), pages 163-192, March.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:1:d:10.1007_s11634-023-00566-2
    DOI: 10.1007/s11634-023-00566-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-023-00566-2
    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/s11634-023-00566-2?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. A. G. Constantine & J. C. Gower, 1978. "Graphical Representation of Asymmetric Matrices," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 297-304, November.
    2. Donatella Vicari, 2018. "CLUSKEXT: CLUstering model for SKew-symmetric data including EXTernal information," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 43-64, March.
    3. John C. Gower, 2018. "Skew symmetry in retrospect," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 33-41, March.
    4. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    5. Donatella Vicari, 2014. "Classification of Asymmetric Proximity Data," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 386-420, October.
    6. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    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. Naoto Yamashita & Shin-ichi Mayekawa, 2015. "A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(3), pages 243-266, September.
    2. Giuseppe Bove & Akinori Okada, 2018. "Methods for the analysis of asymmetric pairwise relationships," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 5-31, March.
    3. Rosaria Lombardo & Ida Camminatiello & Eric J. Beh, 2019. "Assessing Satisfaction with Public Transport Service by Ordered Multiple Correspondence Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 143(1), pages 355-369, May.
    4. Kyusoon Kim & Hee‐Seok Oh & Minsu Park, 2023. "Principal component analysis for river network data: Use of spatiotemporal correlation and heterogeneous covariance structure," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    5. Christina Yassouridis & Friedrich Leisch, 2017. "Benchmarking different clustering algorithms on functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 467-492, September.
    6. ten Berge, Jos M. F., 1997. "Reduction of asymmetry by rank-one matrices," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 357-366, May.
    7. Pieter C. Schoonees & Patrick J. F. Groenen & Michel Velden, 2022. "Least-squares bilinear clustering of three-way data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 1001-1037, December.
    8. Wu, Han-Ming & Tien, Yin-Jing & Chen, Chun-houh, 2010. "GAP: A graphical environment for matrix visualization and cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 767-778, March.
    9. Sewell, Daniel K., 2018. "Visualizing data through curvilinear representations of matrices," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 255-270.
    10. José E. Chacón, 2021. "Explicit Agreement Extremes for a 2 × 2 Table with Given Marginals," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 257-263, July.
    11. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 235-260, June.
    12. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    13. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    14. Amiri, Babak & Karimianghadim, Ramin, 2024. "A novel text clustering model based on topic modelling and social network analysis," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    15. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    16. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    17. A van Giessen & K G M Moons & G A de Wit & W M M Verschuren & J M A Boer & H Koffijberg, 2015. "Tailoring the Implementation of New Biomarkers Based on Their Added Predictive Value in Subgroups of Individuals," PLOS ONE, Public Library of Science, vol. 10(1), pages 1-14, January.
    18. Adele Ravagnani & Fabrizio Lillo & Paola Deriu & Piero Mazzarisi & Francesca Medda & Antonio Russo, 2024. "Dimensionality reduction techniques to support insider trading detection," Papers 2403.00707, arXiv.org, revised May 2024.
    19. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    20. Alfredo García-Hiernaux & José Casals & Miguel Jerez, 2012. "Estimating the system order by subspace methods," Computational Statistics, Springer, vol. 27(3), pages 411-425, September.

    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:advdac:v:18:y:2024:i:1:d:10.1007_s11634-023-00566-2. 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.