A Generic Disjunctive/Conjunctive Decomposition Model forn-ary Relations

✍ Scribed by Iwin Leenen; Iven Van Mechelen; Paul De Boeck

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 201 KB
• Volume: 43
• Category: Article
• ISSN: 0022-2496
• DOI: 10.1006/jmps.1998.1226

✦ Synopsis

This paper discusses a generic decomposition model that represents an arbitrary n-ary relation as a disjunctive or conjunctive combination of a number of n-ary component relations of a prespecified type. An important subclass of order-preserving decompositions is defined and its properties are derived. The generic model is shown to subsume various known models as special cases, including the models of Boolean factor analysis, hierarchical classes analysis, and disjunctiveÂconjunctive nonmetric factor analysis. Moreover, it also subsumes a broad range of new models as exemplified with a novel model for multidimensional parallelogram analysis and novel threeway extensions of nonmetric factor analysis.