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Reduced $$k$$ k -means clustering with MCA in a low-dimensional space

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  • Masaki Mitsuhiro
  • Hiroshi Yadohisa

Abstract

In the two-step sequential approach called tandem analysis, we focus on applying a clustering algorithm on estimated object scores after dimensional reduction of variables. In this approach, reduction may obscure or mask taxonomic information (Arabie and Hubert in Handbook of marketing research. Blackwell, Oxford, 1994 ). As an alternative to tandem analysis, an approach combining two methods for categorical data is proposed by Hwang et al. (Psychometrika 71:161–171, 2006 ); however, this method does not consider the removal of object scores estimated as a vector of $$1$$ 1 that has no meaning in the first dimension. In this study, we propose a method for clustering objects consisting of categorical variables in a low-dimensional space. Our proposed method uses simultaneous analysis of multi-dimensional nonmetric principal component analysis and $$k$$ k -means clustering for categorical data; that is, we reduce dimensions with category quantifications, thus clustering object scores. We display object scores and variable categories, and therefore, every relationship between objects and categories can be interpreted for each cluster. Using simulated data, this method has been compared with tandem clustering and applied to real world data. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:2:p:463-475
    DOI: 10.1007/s00180-014-0544-8
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    References listed on IDEAS

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    1. 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.
    2. Alfonso Iodice D’Enza & Francesco Palumbo, 2013. "Iterative factor clustering of binary data," Computational Statistics, Springer, vol. 28(2), pages 789-807, April.
    3. 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.
    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. 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. Stef Buuren & Willem Heiser, 1989. "Clusteringn objects intok groups under optimal scaling of variables," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 699-706, September.
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