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Author: Giovanni Rossi

Affiliation: University of Bologna, Italy

ISBN: 978-989-758-157-1

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 the appropriate number of clusters is implicitly extracted from the given data set. (More)

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Paper citation in several formats:
Rossi, G. (2015). Multilinear Objective Function-based Clustering.In Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (ECTA 2015) ISBN 978-989-758-157-1, pages 141-149. DOI: 10.5220/0005592701410149

@conference{fcta15,
author={Giovanni Rossi.},
title={Multilinear Objective Function-based Clustering},
booktitle={Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (ECTA 2015)},
year={2015},
pages={141-149},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005592701410149},
isbn={978-989-758-157-1},
}

TY - CONF

JO - Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (ECTA 2015)
TI - Multilinear Objective Function-based Clustering
SN - 978-989-758-157-1
AU - Rossi, G.
PY - 2015
SP - 141
EP - 149
DO - 10.5220/0005592701410149

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