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 [8]. 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 [1].
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Masís, D., Segura, E., Trejos, J., Xavier, A. (2023). Fuzzy Clustering by Hyperbolic Smoothing. In: Brito, P., Dias, J.G., Lausen, B., Montanari, A., Nugent, R. (eds) Classification and Data Science in the Digital Age. IFCS 2022. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-031-09034-9_27
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