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Fuzzy clustering with structural constraints

✍ Scribed by Victor Chepoi; Dan Dumitrescu

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 510 KB
Volume: 105
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(97)00256-x

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✦ Synopsis

In this paper we propose a generalization of the standard clustering problem, which we call Structural Constrained Clustering (SCC) problem. In SCC problem, the cluster interconnections are given by a binary relation R. If this relation is empty then SCC problem reduces to the standard classification problem. The cluster structure imposed by R may be described by the covering graph of R. For example, if this graph is a rooted tree then a hierarchical structure is imposed to the clusters.

We formulate SCC as a fuzzy clustering problem with prototype inter-relation. A general algorithm to solve this problem is proposed. For three particular distance measures (squared, Euclidean and Ll metric) we compute the prototypes by solving a particular multifacility location problem.

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