Author:
Giovanni Rossi
Affiliation:
University of Bologna, Italy
Keyword(s):
Fuzzy Clustering, Similarity Matrix, Pseudo-Boolean Function, Multilinear Extension, Local Search.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Computational Intelligence
;
Fuzzy Information Processing, Fusion, Text Mining
;
Fuzzy Information Retrieval and Data Mining
;
Fuzzy Systems
;
Fuzzy Systems Design, Modeling and Control
;
Pattern Recognition: Fuzzy Clustering and Classifiers
;
Soft Computing
Abstract:
The input of most clustering algorithms is a symmetric matrix quantifying similarity within data pairs. Such
a matrix is here turned into a quadratic set function measuring cluster score or similarity within data subsets
larger than pairs. In general, any set function reasonably assigning a cluster score to data subsets gives rise to an
objective function-based clustering problem. When considered in pseudo-Boolean form, cluster score enables
to evaluate fuzzy clusters through multilinear extension MLE, while the global score of fuzzy clusterings
simply is the sum over constituents fuzzy clusters of their MLE score. This is shown to be no greater than the
global score of hard clusterings or partitions of the data set, thereby expanding a known result on extremizers of
pseudo-Boolean functions. Yet, a multilinear objective function allows to search for optimality in the interior
of the hypercube. The proposed method only requires a fuzzy clustering as initial candidate solution, for th
e
appropriate number of clusters is implicitly extracted from the given data set.
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