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Algorithms for additive clustering of rectangular data tables

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  • Depril, Dirk
  • Van Mechelen, Iven
  • Mirkin, Boris

Abstract

The overlapping additive clustering model or principal cluster model is a model for two-way two-mode object by variable data that implies an overlapping clustering of the objects and a set of profiles (characteristic variable values for each cluster). The model values of the variables of an object are the sum of the profiles of its corresponding clusters. In the associated data analysis the data matrix at hand is approximated by an overlapping additive clustering model of a prespecified rank by minimizing a least squares loss function. Recently an algorithm has been proposed for this purpose. This algorithm is a sequential fitting strategy, also called the method of principal clusters (PCL). Theoretical and empirical evidence that the PCL algorithm may have problems in revealing the true structure underlying a data set will be presented. As a way out, three new algorithms to fit the principal cluster model to empirical data will be presented: two of an alternating least squares (ALS) type, orthogonally combined with two different starting strategies, and one based on simulated annealing (SA). In a simulation study it is demonstrated that all three new algorithms outperform the existing PCL algorithm. The amount of objects that belong to more than one cluster (the overlap) is further found to have a considerable influence on the algorithmic performance of the ALS algorithms, with low amounts of overlap requiring a different starting strategy than high ones. As a consequence, for the analysis of real data sets in practice, a hybrid approach will be presented consisting of one of the ALS algorithms initialized by means of the two starting strategies under study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:11:p:4923-4938
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    References listed on IDEAS

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    1. Van Mechelen, Iven & Schepers, Jan, 2007. "A unifying model involving a categorical and/or dimensional reduction for multimode data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 537-549, September.
    2. Boris Mirkin, 1990. "A sequential fitting procedure for linear data analysis models," Journal of Classification, Springer;The Classification Society, vol. 7(2), pages 167-195, September.
    3. 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. Doove, Lisa L. & Wilderjans, Tom F. & Calcagnì, Antonio & Van Mechelen, Iven, 2017. "Deriving optimal data-analytic regimes from benchmarking studies," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 81-91.
    2. Julian Rossbroich & Jeffrey Durieux & Tom F. Wilderjans, 2022. "Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 264-301, July.
    3. 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.
    4. Boris Mirkin & Soroosh Shalileh, 2022. "Community Detection in Feature-Rich Networks Using Data Recovery Approach," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 432-462, November.
    5. Chiheb-Eddine N’Cir & Nadia Essoussi & Mohamed Limam, 2015. "Kernel-Based Methods to Identify Overlapping Clusters with Linear and Nonlinear Boundaries," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 176-211, July.
    6. 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.

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