FINDCLUS: Fuzzy INdividual Differences CLUStering

• Published in: Journal of classification Vol. 29; no. 2; pp. 170 - 198
• Main Authors: Giordani, Paolo, Kiers, Henk A.L.
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.07.2012; Springer Nature B.V
• Subjects: Algorithms; Bioinformatics; Cluster analysis; Clustering; Data analysis; Fuzzy logic; Marketing; Mathematics and Statistics; Pattern Recognition; Psychometrics; Signal,Image and Speech Processing; Statistical Theory and Methods; Statistics; INDCLUS; Fuzzy approach; Three-way analysis; Proximity data; Clustering
• ISSN: 0176-4268; 1432-1343
• DOI: 10.1007/s00357-012-9109-0

ADditive CLUStering (ADCLUS) is a tool for overlapping clustering of two-way proximity matrices (objects × objects). In Simple Additive Fuzzy Clustering (SAFC), a variant of ADCLUS is introduced providing a fuzzy partition of the objects, that is the objects belong to the clusters with the so-called membership degrees ranging from zero (complete non-membership) to one (complete membership). INDCLUS (INdividual Differences CLUStering) is a generalization of ADCLUS for handling three-way proximity arrays (objects × objects × subjects). Here, we propose a fuzzified alternative to INDCLUS capable to offer a fuzzy partition of the objects by generalizing in a three-way context the idea behind SAFC. This new model is called Fuzzy INdividual Differences CLUStering (FINDCLUS). An algorithm is provided for fitting the FINDCLUS model to the data. Finally, the results of a simulation experiment and some applications to synthetic and real data are discussed.