Additive clustering: Representation of similarities as combinations of discrete overlapping properties

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Abstract

For the discovery and representation of structures in similarity data, an alternative to the inherently continuous spatial models of multidimensional scaling and factor analysis and to the strictly hierarchical models of discrete clustering is presented. It is assumed that the effective similarity of any 2 objects is a simple additive function of underlying weights associated with whatever properties are shared by both objects. Based on this model, a method of additive clustering, ADCLUS, is described that is capable of estimating (a) which subsets of a given set of objects correspond to positively weighted properties, and (b) the numerical values of those weights. The method subsumes hierarchical clustering as a special case and can be regarded as a discrete analog of principal components analysis. Applications to several diverse types of data are presented, and the bearing of the results on current theoretical issues concerning distinctive features and the adequacy of purely hierarchical models is discussed. (4 p ref) (PsycINFO Database Record (c) 2006 APA, all rights reserved)

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