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Lowdimensional Additive Overlapping Clustering

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  • Dirk Depril
  • Iven Mechelen
  • Tom Wilderjans

Abstract

To reveal the structure underlying two-way two-mode object by variable data, Mirkin (1987) has proposed an additive overlapping clustering model. This model implies an overlapping clustering of the objects and a reconstruction of the data, with the reconstructed variable profile of an object being a summation of the variable profiles of the clusters it belongs to. Grasping the additive (overlapping) clustering structure of object by variable data may, however, be seriously hampered in case the data include a very large number of variables. To deal with this problem, we propose a new model that simultaneously clusters the objects in overlapping clusters and reduces the variable space; as such, the model implies that the cluster profiles and, hence, the reconstructed data profiles are constrained to lie in a lowdimensional space. An alternating least squares (ALS) algorithm to fit the new model to a given data set will be presented, along with a simulation study and an illustrative example that makes use of empirical data. Copyright Springer Science+Business Media, LLC 2012

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  • 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.
    • Handle: RePEc:spr:jclass:v:29:y:2012:i:3:p:297-320
    DOI: 10.1007/s00357-012-9112-5
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    1. Wei‐Chien Chang, 1983. "On Using Principal Components before Separating a Mixture of Two Multivariate Normal Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(3), pages 267-275, November.
    2. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    3. 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.
    4. Douglas Steinley & Michael J. Brusco, 2007. "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 99-121, June.
    5. Tom Wilderjans & E. Ceulemans & I. Mechelen, 2012. "The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 724-740, October.
    6. Roberto Rocci & Maurizio Vichi, 2005. "Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 715-736, December.
    7. Lawrence Hubert & Phipps Arabie & Matthew Hesson-Mcinnis, 1992. "Multidimensional scaling in the city-block metric: A combinatorial approach," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 211-236, December.
    8. Eva Ceulemans & Iven Mechelen, 2005. "Hierarchical classes models for three-way three-mode binary data: interrelations and model selection," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 461-480, September.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Maurizio Vichi & Roberto Rocci & Henk A.L. Kiers, 2007. "Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 71-98, June.
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    Cited by:

    1. 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.

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