MAPCLUS: A mathematical programming approach to fitting the ADCLUS model. We present a new algorithm, MAPCLUS (MAthematicalProgrammingCLUStering), for fitting the Shepard-Arabie ADCLUS (forADditiveCLUStering) model. MAPCLUS utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach, to impose discrete (0,1) constraints on parameters defining cluster membership. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, we consider an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividualDifferencesCLUStering).

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  1. Bocci, Laura; Vicari, Donatella: ROOTCLUS: searching for “ROOT clusters” in three-way proximity data (2019)
  2. Bove, Giuseppe; Okada, Akinori: Methods for the analysis of asymmetric pairwise relationships (2018)
  3. Bocci, Laura; Vicari, Donatella: GINDCLUS: generalized INDCLUS with external information (2017)
  4. France, Stephen L.; Chen, Wen; Deng, Yumin: ADCLUS and INDCLUS: analysis, experimentation, and meta-heuristic algorithm extensions (2017)
  5. Hansen, Pierre; Meyer, Christophe: A polynomial algorithm for a class of 0-1 fractional programming problems involving composite functions, with an application to additive clustering (2014)
  6. Blanchard, Simon J.; Desarbo, Wayne S.: A new zero-inflated negative binomial methodology for latent category identification (2013)
  7. Heiser, Willem J.: In memoriam, J. Douglas Carroll 1939--2011 (2013)
  8. Giordani, Paolo; Kiers, Henk A. L.: FINDCLUS: fuzzy individual differences clustering (2012)
  9. Heiser, Willem J.: In memoriam: J. Douglas Carroll, 1939--2011 (2012)
  10. Vrac, M.; Billard, L.; Diday, E.; Chédin, A.: Copula analysis of mixture models (2012)
  11. Wilderjans, Tom F.; Depril, Dirk; Van Mechelen, Iven: Block-relaxation approaches for fitting the INDCLUS model (2012)
  12. Vicari, Donatella; Vichi, Maurizio: Structural classification analysis of three-way dissimilarity data (2009)
  13. Yokoyama, Satoru; Nakayama, Astudo; Okada, Akinori: One mode three-way overlapping cluster analysis (2009)
  14. Bocci, Laura; Vicari, Donatella; Vichi, Maurizio: A mixture model for the classification of three-way proximity data (2006)
  15. Lee, Michael D.: On the complexity of additive clustering models (2001)
  16. Leenen, Iwin; van Mechelen, Iven; De Boeck, Paul; Rosenberg, Seymour: INDCLAS: a three-way hierarchical classes model (1999)
  17. Vichi, Maurizio: Principal classifications analysis: a method for generating consensus dendrograms and its application to three-way data. (1998)
  18. Kiers, Henk A. L.: A modification of the SINDCLUS algorithm for finding the ADCLUS and INCLUS models (1997)
  19. Gordon, A. D.: A survey of constrained classification (1996)
  20. Carroll, J. Douglas; Corter, James E.: A graph-theoretic method for organizing overlapping clusters into trees, multiple trees, or extended trees (1995)

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