Fuzzy Clustering by Hyperbolic Smoothing

• URL: http://arxiv.org/abs/2207.04261v1
• Date: Sat, 9 Jul 2022 12:40:46 GMT
• Title: Fuzzy Clustering by Hyperbolic Smoothing
• Authors: David Masis, Esteban Segura, Javier Trejos, Adilson Xavier
• Abstract summary: We propose a novel method for building fuzzy clusters of large data sets, using a smoothing numerical approach. The smoothing allows a conversion from a strongly non-differentiable problem into differentiable subproblems of optimization without constraints of low dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We propose a novel method for building fuzzy clusters of large data sets, using a smoothing numerical approach. The usual sum-of-squares criterion is relaxed so the search for good fuzzy partitions is made on a continuous space, rather than a combinatorial space as in classical methods \cite{Hartigan}. The smoothing allows a conversion from a strongly non-differentiable problem into differentiable subproblems of optimization without constraints of low dimension, by using a differentiable function of infinite class. For the implementation of the algorithm we used the statistical software $R$ and the results obtained were compared to the traditional fuzzy $C$--means method, proposed by Bezdek.

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