An error variance approach to two-mode hierarchical clustering |
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Authors: | Thomas Eckes Peter Orlik |
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Affiliation: | 1. Fachbereich 1, Bergische Universit?t Wuppertal, Gau?str. 20, D-5600, Wuppertal 1, Germany 2. Fachrichtung Psychologie, Universit?t des Saarlandes, Im Stadtwald, D-6600, Saarbrücken, Germany
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Abstract: | A new agglomerative method is proposed for the simultaneous hierarchical clustering of row and column elements of a two-mode
data matrix. The procedure yields a nested sequence of partitions of the union of two sets of entities (modes). A two-mode
cluster is defined as the union of subsets of the respective modes. At each step of the agglomerative process, the algorithm
merges those clusters whose fusion results in the smallest possible increase in an internal heterogeneity measure. This measure
takes into account both the variance within the respective cluster and its centroid effect defined as the squared deviation
of its mean from the maximum entry in the input matrix. The procedure optionally yields an overlapping cluster solution by
assigning further row and/or column elements to clusters existing at a preselected hierarchical level. Applications to real
data sets drawn from consumer research concerning brand-switching behavior and from personality research concerning the interaction
of behaviors and situations demonstrate the efficacy of the method at revealing the underlying two-mode similarity structure. |
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Keywords: | Clustering Two-mode data Ultrametric representation Agglomerative algorithm Heterogeneity index Brand-switching Behavior-situation congruence |
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