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Block-Relaxation Approaches for Fitting the INDCLUS Model

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  • Tom Wilderjans
  • Dirk Depril
  • Iven Mechelen

Abstract

A well-known clustering model to represent I × I × J data blocks, the J frontal slices of which consist of I × I object by object similarity matrices, is the INDCLUS model. This model implies a grouping of the I objects into a prespecified number of overlapping clusters, with each cluster having a slice-specific positive weight. An INDCLUS model is fitted to a given data set by means of minimizing a least squares loss function. The minimization of this loss function has appeared to be a difficult problem for which several algorithmic strategies have been proposed. At present, the best available option seems to be the SYMPRES algorithm, which minimizes the loss function by means of a block-relaxation algorithm. Yet, SYMPRES is conjectured to suffer from a severe local optima problem. As a way out, based on theoretical results with respect to optimally designing block-relaxation algorithms, five alternative block-relaxation algorithms are proposed. In a simulation study it appears that the alternative algorithms with overlapping parameter subsets perform best and clearly outperform SYMPRES in terms of optimization performance and cluster recovery. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Tom Wilderjans & Dirk Depril & Iven Mechelen, 2012. "Block-Relaxation Approaches for Fitting the INDCLUS Model," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 277-296, October.
    • Handle: RePEc:spr:jclass:v:29:y:2012:i:3:p:277-296
    DOI: 10.1007/s00357-012-9113-4
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    References listed on IDEAS

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    1. J. Carroll & Phipps Arabie, 1983. "Indclus: An individual differences generalization of the adclus model and the mapclus algorithm," Psychometrika, Springer;The Psychometric Society, vol. 48(2), pages 157-169, June.
    2. Wilderjans, Tom & Ceulemans, Eva & Van Mechelen, Iven, 2009. "Simultaneous analysis of coupled data blocks differing in size: A comparison of two weighting schemes," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1086-1098, February.
    3. Depril, Dirk & Van Mechelen, Iven & Mirkin, Boris, 2008. "Algorithms for additive clustering of rectangular data tables," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4923-4938, July.
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    6. Eva Ceulemans & Iven Mechelen & Iwin Leenen, 2007. "The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 377-391, September.
    7. G. O. Roberts & S. K. Sahu, 1997. "Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 291-317.
    8. Anil Chaturvedi & J. Carroll, 1994. "An alternating combinatorial optimization approach to fitting the INDCLUS and generalized INDCLUS models," Journal of Classification, Springer;The Classification Society, vol. 11(2), pages 155-170, September.
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    Cited by:

    1. Laura Bocci & Donatella Vicari, 2019. "ROOTCLUS: Searching for “ROOT CLUSters” in Three-Way Proximity Data," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 941-985, December.
    2. Laura Bocci & Donatella Vicari, 2017. "GINDCLUS: Generalized INDCLUS with External Information," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 355-381, June.

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