MAPCLUS swMATH ID: 20021 Software Authors: Arabie, Phipps; Carroll, J.Douglas Description: 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). Homepage: http://link.springer.com/article/10.1007/BF02294077 Related Software: Indclus; FINDCLUS; PARAFAC; ROOTCLUS; asymmetry; smacof; ez; OHSUMED; pertsaus2; BayesDA; clusfind; UCI-ml; AS 136; ADDTREE/P; KYST; Matlab; Algorithm 457; ALSCAL Cited in: 30 Documents all top 5 Cited by 39 Authors 4 Vicari, Donatella 3 Bocci, Laura 3 Carroll, J. Douglas 3 Vichi, Maurizio 2 Bove, Giuseppe 2 Heiser, Willem J. 2 Kiers, Henk A. L. 2 Mirkin, Boris G. 2 Okada, Akinori 2 Van Mechelen, Iven 1 Billard, Lynne 1 Blanchard, Simon J. 1 Chaturvedi, Anil D. 1 Chédin, A. 1 Clark, Linda A. 1 Corter, James E. 1 Dailey, David P. 1 De Boeck, Paul 1 Deng, Yumin 1 Depril, Dirk 1 DeSarbo, Wayne S. 1 Di Ciaccio, Agostino 1 Diday, Edwin 1 France, Stephen L. 1 Gaul, Wolfgang 1 Giordani, Paolo E. 1 Hansen, Pierre 1 Lee, Michael D. 1 Leenen, Iwin 1 Lefkovitch, L. P. 1 Meyer, Christophe 1 Nakayama, Astudo 1 Ozawa, Kazumasa 1 Rosenberg, Seymour 1 Schader, Martin 1 Vrac, M. 1 Wilderjans, Tom Frans 1 Yokoyama, Satoru 1 Zahorik, Anthony J. all top 5 Cited in 10 Serials 11 Journal of Classification 5 Psychometrika 4 Computational Statistics and Data Analysis 2 Computational Statistics 2 Advances in Data Analysis and Classification. ADAC 1 Discrete Mathematics 1 Mathematical Biosciences 1 Journal of Mathematical Psychology 1 European Journal of Operational Research 1 Pattern Recognition all top 5 Cited in 7 Fields 24 Statistics (62-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Combinatorics (05-XX) 2 History and biography (01-XX) 2 Operations research, mathematical programming (90-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) Citations by Year