Three-way fuzzy clustering models for LR fuzzy time trajectories

Authors:
Renato Coppi;Pierpaolo D'Urso
Affiliations:
Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università degli Studi di Roma, "La Sapienza", P.le A. Moro, 5 - 00185 Roma, Italy;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università degli Studi di Roma, "La Sapienza", P.le A. Moro, 5 - 00185 Roma, Italy
Venue:
Computational Statistics & Data Analysis
Year:
2003

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Abstract

Fuzzy multivariate time trajectories are defined. For a suitable class, called LR time trajectories, three types of dissimilarity measures are introduced: the instantaneous, the velocity and the simultaneous measures, respectively. Correspondingly, three different kinds of dynamic fuzzy clustering models are suggested, based on a generalization of the Bezdek and Yang and Ko objective functions for fuzzy clustering. The solutions and characteristics of the three models are then illustrated. A comparative appraisal of their practical meaning is proposed by means of an application to the time pattern of the subjective judgments expressed by a sample of web navigators on different types of banners. Some indications for future research in this methodological domain are finally provided.