IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v9y2015i3p243-266.html
   My bibliography  Save this article

A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

Author

Listed:
  • Naoto Yamashita
  • Shin-ichi Mayekawa

Abstract

Biplot is a technique for obtaining a low-dimensional configuration of the data matrix in which both the objects and the variables of the data matrix are jointly represented as points and vectors, respectively. However, biplots with a large number of objects and variables remain difficult to interpret. Therefore, in this research, we propose a new biplot procedure that allows us to interpret a large data matrix. In particular, the objects and variables are classified into a small number of clusters by using fuzzy $$c$$ c -means clustering and the resulting clusters are simultaneously biplotted in lower-dimensional space. This procedure allows us to understand the configurations easily and to grasp the fuzzy memberships of the objects and variables to the clusters. A simulation study and real data example are also provided to demonstrate the effectiveness of the proposed procedure. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:9:y:2015:i:3:p:243-266
    DOI: 10.1007/s11634-014-0184-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11634-014-0184-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11634-014-0184-4?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. Heungsun Hwang & Wayne Desarbo & Yoshio Takane, 2007. "Fuzzy Clusterwise Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 181-198, June.
    2. Hye Suk & Heungsun Hwang, 2010. "Regularized fuzzy clusterwise ridge regression," 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. 4(1), pages 35-51, April.
    3. Roubens, Marc, 1982. "Fuzzy clustering algorithms and their cluster validity," European Journal of Operational Research, Elsevier, vol. 10(3), pages 294-301, July.
    4. Jos Berge, 1983. "A generalization of Kristof's theorem on the trace of certain matrix products," Psychometrika, Springer;The Psychometric Society, vol. 48(4), pages 519-523, December.
    5. 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.
    6. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    7. Roberto Rocci & Maurizio Vichi, 2005. "Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 715-736, December.
    8. Kohei Adachi, 2011. "Constrained principal component analysis of standardized data for biplots with unit-length variable vectors," 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. 5(1), pages 23-36, April.
    9. 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.
    10. Coppi, Renato & Gil, Maria A. & Kiers, Henk A.L., 2006. "The fuzzy approach to statistical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 1-14, November.
    11. Maurizio Vichi & Roberto Rocci & Henk A.L. Kiers, 2007. "Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 71-98, June.
    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. Naoto Yamashita, 2023. "Principal component analysis constrained by layered simple structures," 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(2), pages 347-367, June.
    2. Pierpaolo D’Urso & María Ángeles Gil, 2017. "Fuzzy data analysis and classification," 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(4), pages 645-657, December.
    3. Naoto Yamashita & Kohei Adachi, 2020. "A Modified k-Means Clustering Procedure for Obtaining a Cardinality-Constrained Centroid Matrix," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 509-525, July.
    4. Julio César Hernández-Sánchez & José Luis Vicente-Villardón, 2017. "Logistic biplot for nominal 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(2), pages 307-326, June.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Dirk Depril & Iven Mechelen & Tom Wilderjans, 2012. "Lowdimensional Additive Overlapping Clustering," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 297-320, October.
    6. Xavier Bry & Ndèye Niang & Thomas Verron & Stéphanie Bougeard, 2023. "Clusterwise elastic-net regression based on a combined information criterion," 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(1), pages 75-107, March.
    7. Luca Greco & Antonio Lucadamo & Pietro Amenta, 2020. "An Impartial Trimming Approach for Joint Dimension and Sample Reduction," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 769-788, October.
    8. Tianyu Tan & Hye Suk & Heungsun Hwang & Jooseop Lim, 2013. "Functional fuzzy clusterwise regression analysis," 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. 7(1), pages 57-82, March.
    9. Michio Yamamoto & Heungsun Hwang, 2017. "Dimension-Reduced Clustering of Functional Data via Subspace Separation," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 294-326, July.
    10. Uno, Kohei & Satomura, Hironori & Adachi, Kohei, 2016. "Fixed factor analysis with clustered factor score constraint," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 265-274.
    11. Vichi, Maurizio & Saporta, Gilbert, 2009. "Clustering and disjoint principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3194-3208, June.
    12. 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.
    13. 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.
    14. M. Velden & A. Iodice D’Enza & F. Palumbo, 2017. "Cluster Correspondence Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 158-185, March.
    15. 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.
    16. 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.
    17. Stéphanie Bougeard & Hervé Abdi & Gilbert Saporta & Ndèye Niang, 2018. "Clusterwise analysis for multiblock component methods," 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 285-313, June.
    18. 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.
    19. 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.
    20. Kohei Uno & Kohei Adachi & Nickolay T. Trendafilov, 2019. "Clustered Common Factor Exploration in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1048-1067, December.

    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:9:y:2015:i:3:p:243-266. 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.