IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v82y2017i1d10.1007_s11336-016-9514-0.html
   My bibliography  Save this article

Cluster Correspondence Analysis

Author

Listed:
  • M. Velden

    (Erasmus University Rotterdam)

  • A. Iodice D’Enza

    (Università di Cassino e del Lazio Meridionale)

  • F. Palumbo

    (Università degli Studi di Napoli Federico II)

Abstract

A method is proposed that combines dimension reduction and cluster analysis for categorical data by simultaneously assigning individuals to clusters and optimal scaling values to categories in such a way that a single between variance maximization objective is achieved. In a unified framework, a brief review of alternative methods is provided and we show that the proposed method is equivalent to GROUPALS applied to categorical data. Performance of the methods is appraised by means of a simulation study. The results of the joint dimension reduction and clustering methods are compared with the so-called tandem approach, a sequential analysis of dimension reduction followed by cluster analysis. The tandem approach is conjectured to perform worse when variables are added that are unrelated to the cluster structure. Our simulation study confirms this conjecture. Moreover, the results of the simulation study indicate that the proposed method also consistently outperforms alternative joint dimension reduction and clustering methods.

Suggested Citation

  • M. Velden & A. Iodice D’Enza & F. Palumbo, 2017. "Cluster Correspondence Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 158-185, March.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9514-0
    DOI: 10.1007/s11336-016-9514-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-016-9514-0
    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/s11336-016-9514-0?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. Michel Velden & Tammo Bijmolt, 2006. "Generalized canonical correlation analysis of matrices with missing rows: a simulation study," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 323-331, June.
    2. Michel Velden & Yoshio Takane, 2012. "Generalized canonical correlation analysis with missing values," Computational Statistics, Springer, vol. 27(3), pages 551-571, September.
    3. Alfonso Iodice D’Enza & Francesco Palumbo, 2013. "Iterative factor clustering of binary data," Computational Statistics, Springer, vol. 28(2), pages 789-807, April.
    4. Heungsun Hwang & Hec Montréal & William Dillon & Yoshio Takane, 2006. "An Extension of Multiple Correspondence Analysis for Identifying Heterogeneous Subgroups of Respondents," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 161-171, March.
    5. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    6. Vichi, Maurizio & Kiers, Henk A. L., 2001. "Factorial k-means analysis for two-way data," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 49-64, July.
    7. 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)

    Citations

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


    Cited by:

    1. Izzo, Filomena & Camminatiello, Ida & Sasso, Pasquale & Solima, Ludovico & Lombardo, Rosaria, 2023. "Creating customer, museum and social value through digital technologies: Evidence from the MANN Assiri project," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).
    2. Kensuke Tanioka & Hiroshi Yadohisa, 2019. "Simultaneous Method of Orthogonal Non-metric Non-negative Matrix Factorization and Constrained Non-hierarchical Clustering," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 73-93, April.
    3. Efthymios Costa & Ioanna Papatsouma & Angelos Markos, 2023. "Benchmarking distance-based partitioning methods for mixed-type 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. 17(3), pages 701-724, September.
    4. 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.
    5. Cabral, Laura & Kim, Amy M., 2020. "An empirical reappraisal of the four types of cyclists," Transportation Research Part A: Policy and Practice, Elsevier, vol. 137(C), pages 206-221.
    6. Tamakloe, Reuben & Zhang, Kaihan & Atandzi, Jonathan & Park, Dongjoo, 2024. "Examining urban delivery service user profiles and determinants of drone delivery adoption in Ghana considering usage before and after the COVID-19 pandemic," Transport Policy, Elsevier, vol. 146(C), pages 279-294.

    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. Masaki Mitsuhiro & Hiroshi Yadohisa, 2015. "Reduced $$k$$ k -means clustering with MCA in a low-dimensional space," Computational Statistics, Springer, vol. 30(2), pages 463-475, June.
    2. van de Velden, M. & Iodice D' Enza, A. & Palumbo, F., 2014. "Cluster Correspondence Analysis," Econometric Institute Research Papers EI 2014-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Kensuke Tanioka & Hiroshi Yadohisa, 2019. "Simultaneous Method of Orthogonal Non-metric Non-negative Matrix Factorization and Constrained Non-hierarchical Clustering," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 73-93, April.
    4. Monia Ranalli & Roberto Rocci, 2017. "A Model-Based Approach to Simultaneous Clustering and Dimensional Reduction of Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1007-1034, December.
    5. Alfonso Iodice D’Enza & Francesco Palumbo, 2013. "Iterative factor clustering of binary data," Computational Statistics, Springer, vol. 28(2), pages 789-807, April.
    6. DeSarbo, Wayne S. & Selin Atalay, A. & Blanchard, Simon J., 2009. "A three-way clusterwise multidimensional unfolding procedure for the spatial representation of context dependent preferences," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3217-3230, June.
    7. Roberto Rocci & Stefano Gattone & Maurizio Vichi, 2011. "A New Dimension Reduction Method: Factor Discriminant K-means," Journal of Classification, Springer;The Classification Society, vol. 28(2), pages 210-226, July.
    8. 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.
    9. Donatella Vicari & Paolo Giordani, 2023. "CPclus: Candecomp/Parafac Clustering Model for Three-Way Data," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 432-465, July.
    10. Michael C. Thrun & Alfred Ultsch, 2021. "Using Projection-Based Clustering to Find Distance- and Density-Based Clusters in High-Dimensional Data," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 280-312, July.
    11. Michio Yamamoto, 2012. "Clustering of functional data in a low-dimensional subspace," 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. 6(3), pages 219-247, October.
    12. Mario Musella & Ida Camminatiello & Francesco Izzo, 2024. "Caritas’s Work for the Goals of Agenda 2030: A Study on the Services Provided in Campania," Mathematics, MDPI, vol. 12(15), pages 1-17, July.
    13. Seoung Bum Kim & Jung Woo Lee & Sin Young Kim & Deok Won Lee, 2013. "Dental Informatics to Characterize Patients with Dentofacial Deformities," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    14. Cristina Tortora & Paul D. McNicholas & Ryan P. Browne, 2016. "A mixture of generalized hyperbolic factor analyzers," 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. 10(4), pages 423-440, December.
    15. Cristina Tortora & Mireille Gettler Summa & Marina Marino & Francesco Palumbo, 2016. "Factor probabilistic distance clustering (FPDC): a new clustering method," 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. 10(4), pages 441-464, December.
    16. Efthymios Costa & Ioanna Papatsouma & Angelos Markos, 2023. "Benchmarking distance-based partitioning methods for mixed-type 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. 17(3), pages 701-724, September.
    17. 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.
    18. Galimberti, Giuliano & Soffritti, Gabriele, 2007. "Model-based methods to identify multiple cluster structures in a data set," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 520-536, September.
    19. Danley, Brian, 2019. "Forest owner objectives typologies: Instruments for each owner type or instruments for most owner types?," Forest Policy and Economics, Elsevier, vol. 105(C), pages 72-82.
    20. Timmerman, Marieke E. & Ceulemans, Eva & Kiers, Henk A.L. & Vichi, Maurizio, 2010. "Factorial and reduced K-means reconsidered," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1858-1871, July.

    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:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9514-0. 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.