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  • nonhierarchical clustering  (2)
  • Expert systems  (1)
  • Hierarchical clustering  (1)
  • 1
    ISSN: 1432-1343
    Keywords: Hierarchical clustering ; Path length trees ; Mathematical programming ; Constrained classification methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A mathematical programming algorithm is developed for fitting ultrametric or additive trees to proximity data where external constraints are imposed on the topology of the tree. The two procedures minimize a least squares loss function. The method is illustrated on both synthetic and real data. A constrained ultrametric tree analysis was performed on similarities between 32 subjects based on preferences for ten odors, while a constrained additive tree analysis was carried out on some proximity data between kinship terms. Finally, some extensions of the methodology to other tree fitting procedures are mentioned.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Psychometrika 45 (1980), S. 211-235 
    ISSN: 1860-0980
    Keywords: additive clustering ; nonhierarchical clustering ; alternating least squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract 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).
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Psychometrika 48 (1983), S. 157-169 
    ISSN: 1860-0980
    Keywords: additive clustering ; nonhierarchical clustering ; combinatorial optimization ; three-way clustering ; individual differences clustering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract We present a new model and associated algorithm, INDCLUS, that generalizes the Shepard-Arabie ADCLUS (ADditive CLUStering) model and the MAPCLUS algorithm, so as to represent in a clustering solution individual differences among subjects or other sources of data. Like MAPCLUS, the INDCLUS generalization 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. All subjects in an INDCLUS analysis are assumed to have a common set of clusters, which are differentially weighted by subjects in order to portray individual differences. As such, INDCLUS provides a (discrete) clustering counterpart to the Carroll-Chang INDSCAL model for (continuous) spatial representations. Finally, we consider possible generalizations of the INDCLUS model and algorithm.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Annals of mathematics and artificial intelligence 2 (1990), S. 77-92 
    ISSN: 1573-7470
    Keywords: Expert systems ; knowledge acquisition ; multiple experts ; multidimensional scaling ; clustering ; trees ; unfolding methods ; data analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Theknowledge transfer problem in artificial intelligence consists of finding effective ways to elicit information from a human expert and represent it in a form suitable for use by an expert system. One approach to formalizing and guiding this knowledge transfer process for certain types of expert systems is to use psychometric scaling methods to analyze data on how the human expert compares or groups solutions. For example, Butler and Corter [1] obtained judgments of thesubstitutability of solutions from an expert, then analyzed the resulting data via techniques for fitting trees and extended trees [2]. The expert's interpretation of certain aspects of the solutions were directly encoded as production rules, allowing rapid prototyping. In this paper we consider the problem of combining information from multiple experts. We propose the use of three-way or “individual differences” multidimensional scaling, tree-fitting, and unfolding models to analyze two types of data obtainable from the multiple experts: judgments of the substitutability of pairs of solutions, and judgments of the appropriateness of specific solutions to specific problems. An application is described in which substitutability data were obtained from three experts and analyzed using the SINDSCAL program [3] for three-way multidimensional scaling [4].
    Type of Medium: Electronic Resource
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