Fuzzy Clustering by Hyperbolic Smoothing
This is an incremental improvement for data analysts and researchers working with large-scale fuzzy clustering.
The authors tackled the problem of fuzzy clustering for large datasets by relaxing the sum-of-squares criterion to enable optimization in a continuous space, resulting in a method that outperformed traditional fuzzy C-means in comparisons.
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.