Multilinear Objective Function-based Clustering

Giovanni Rossi

2015

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.

Paper Citation

in Harvard Style

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

in Bibtex Style

@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},
}

in EndNote Style

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