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A class of two-mode clustering algorithms in a fuzzy setting

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  • Ferraro, Maria Brigida
  • Giordani, Paolo
  • Vichi, Maurizio

Abstract

Two-mode clustering consists in simultaneously partitioning modes (e.g., objects and variables) of an observed two-mode data matrix. A class of two-mode clustering algorithms in a fuzzy framework is proposed. Starting from the Double k-Means algorithm, different fuzzy proposals are addressed. The first one is the Fuzzy Double k-Means (FDkM) algorithm, providing two fuzzy partitions, one for each mode. A second proposal is the Fuzzy Double k-Means with polynomial fuzzifiers (FDkMpf) algorithm, a general method that includes the FDkM one as a particular case. Finally, a robust extension is introduced and analyzed by using the concept of noise cluster. The adequacy of the proposed algorithms is checked by means of a simulation and two real-case studies.

Suggested Citation

  • Ferraro, Maria Brigida & Giordani, Paolo & Vichi, Maurizio, 2021. "A class of two-mode clustering algorithms in a fuzzy setting," Econometrics and Statistics, Elsevier, vol. 18(C), pages 63-78.
    • Handle: RePEc:eee:ecosta:v:18:y:2021:i:c:p:63-78
    DOI: 10.1016/j.ecosta.2020.03.006
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    References listed on IDEAS

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    1. Jean-Patrick Baudry & Margarida Cardoso & Gilles Celeux & Maria Amorim & Ana Ferreira, 2015. "Enhancing the selection of a model-based clustering with external categorical variables," 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(2), pages 177-196, June.
    2. Thomas Eckes & Peter Orlik, 1993. "An error variance approach to two-mode hierarchical clustering," Journal of Classification, Springer;The Classification Society, vol. 10(1), pages 51-74, January.
    3. Martella Francesca & Alfò Marco & Vichi Maurizio, 2008. "Biclustering of Gene Expression Data by an Extension of Mixtures of Factor Analyzers," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-21, February.
    4. Bhatia, Parmeet Singh & Iovleff, Serge & Govaert, Gérard, 2017. "blockcluster: An R Package for Model-Based Co-Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i09).
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    Cited by:

    1. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    2. Ferraro, Maria Brigida, 2024. "Fuzzy k-Means: history and applications," Econometrics and Statistics, Elsevier, vol. 30(C), pages 110-123.

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