Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Filippone, M. (2009) Dealing with non-metric dissimilarities in fuzzy central clustering algorithms. International Journal of Approximate Reasoning, 50(2), pp. 363-384. (doi: 10.1016/j.ijar.2008.08.006)

Abstract

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations.

• Item Type: Articles
• Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Approximate Reasoning. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Approximate Reasoning, 50(2), 2009, DOI: 10.1016/j.ijar.2008.08.006
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Filippone, Dr Maurizio
• Authors: Filippone, M.
• Subjects: Q Science > QA Mathematics; Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: International Journal of Approximate Reasoning
• Publisher: Elsevier
• ISSN: 0888-613X
• ISSN (Online): 1873-4731
• Published Online: 05 September 2008
• Copyright Holders: Copyright © 2009 Elsevier
• First Published: First published in International Journal of Approximate Reasoning 50(2):363-384
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher