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Maximal Interaction Two-Mode Clustering

Author

Listed:
  • Jan Schepers

    (Maastricht University
    K.U. Leuven)

  • Hans-Hermann Bock

    (RWTH Aachen University)

  • Iven Mechelen

    (K.U. Leuven)

Abstract

Most classical approaches for two-mode clustering of a data matrix are designed to attain homogeneous row by column clusters (blocks, biclusters), that is, biclusters with a small variation of data values within the blocks. In contrast, this article deals with methods that look for a biclustering with a large interaction between row and column clusters. Thereby an aggregated, condensed representation of the existing interaction structure is obtained, together with corresponding row and column clusters, which both allow a parsimonious visualization and interpretation. In this paper we provide a statistical justification, in terms of a probabilistic model, for a two-mode interaction clustering criterion that has been proposed by Bock (1980). Furthermore, we show that maximization of this criterion is equivalent to minimizing the classical least-squares two-mode partitioning criterion for the double-centered version of the data matrix. The latter implies that the interaction clustering criterion can be optimized by applying classical two-mode partitioning algorithms. We illustrate the usefulness of our approach for the case of an empirical data set from personality psychology and we compare this method with other biclustering approaches where interactions play a role.

Suggested Citation

  • Jan Schepers & Hans-Hermann Bock & Iven Mechelen, 2017. "Maximal Interaction Two-Mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 49-75, April.
    • Handle: RePEc:spr:jclass:v:34:y:2017:i:1:d:10.1007_s00357-017-9226-x
    DOI: 10.1007/s00357-017-9226-x
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    References listed on IDEAS

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    1. Johannes Forkman & Hans-Peter Piepho, 2014. "Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models," Biometrics, The International Biometric Society, vol. 70(3), pages 639-647, September.
    2. Bock, Hans H., 1996. "Probabilistic models in cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 5-28, November.
    3. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    5. Joost Rosmalen & Patrick Groenen & Javier Trejos & William Castillo, 2009. "Optimization Strategies for Two-Mode Partitioning," Journal of Classification, Springer;The Classification Society, vol. 26(2), pages 155-181, August.
    6. Jan Schepers & Eva Ceulemans & Iven Mechelen, 2008. "Selecting Among Multi-Mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 67-85, June.
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    Citations

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    Cited by:

    1. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2021. "REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction," 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. 15(4), pages 987-1013, December.
    2. Haedo, Christian & Mouchart, Michel, 2019. "Two-mode clustering through profiles of regions and sectors," LIDAM Discussion Papers ISBA 2019014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.
    4. Jacques, Julien & Biernacki, Christophe, 2018. "Model-based co-clustering for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 101-115.
    5. Christian Haedo & Michel Mouchart, 2022. "Two-mode clustering through profiles of regions and sectors," Empirical Economics, Springer, vol. 63(4), pages 1971-1996, October.
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