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A clustering that consists of a nested set of clusters may be represented graphically by a tree. In contrast, a clustering
that includes non-nested overlapping clusters (sometimes termed a “nonhierarchical” clustering) cannot be represented by a
tree. Graphical representations of such non-nested overlapping clusterings are usually complex and difficult to interpret.
Carroll and Pruzansky (1975, 1980) suggested representing non-nested clusterings with multiple ultrametric or additive trees.
Corter and Tversky (1986) introduced the extended tree (EXTREE) model, which represents a non-nested structure as a tree plus
overlapping clusters that are represented by marked segments in the tree. We show here that the problem of finding a nested
(i.e., tree-structured) set of clusters in an overlapping clustering can be reformulated as the problem of finding a clique
in a graph. Thus, clique-finding algorithms can be used to identify sets of clusters in the solution that can be represented
by trees. This formulation provides a means of automatically constructing a multiple tree or extended tree representation
of any non-nested clustering. The method, called “clustrees”, is applied to several non-nested overlapping clusterings derived
using the MAPCLUS program (Arabie and Carroll 1980). 相似文献
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