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An Optimized Gradient Dynamic-Neuro-Weighted-Fuzzy Clustering Method: Application in the Nutrition Field

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Abstract

Soft clustering is able to handle overlapping data thanks to membership functions that allow examples to belong to several clusters. However, the formula linking membership functions to centers and the adoption of fixed time steps, when updating the parameters, prevents research from exploring areas that may be promising. To alleviate this complexity and enlarge the search space, we propose a constrained optimization model that de-assigns memberships from centers. To take advantage of the ability of neural networks to understand the characteristics of the data and of dynamic systems to remember previous groupings, we solve the proposed model by the third-order gradient recurrent network whose stability point is formed by the memberships and the centers. In this respect, the fixed time step Euler-Cauchy algorithm prevents the search from exploring promising regions. To remedy this problem, we adopt a variable time step that allows a maximum decay of the Lyaponuv function at each iteration. We demonstrate that dissociating the membership coefficients from the group centers results in a less complex optimization model with a larger set of feasible solutions offering better optimal fuzzy clustering. We compared our method to different clustering methods basing on silhouette, separability, compactness criterion, and on Dunn’s index; our method has shown its superiority on academic data sets. We used our method to group plants based on 24 nutrients which results in a better classification in comparison with the unidimensional methods.

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Acknowledgements

This work was supported by Ministry of National Education, Professional Training, Higher Education and Scientific Research and the Digital Development Agency (DDA) and CNRST of Morocco (Nos. Alkhawarizmi/2020/23).

Funding

This work is supported by the National Center for Scientific and Technical Research of Morocco via AL-Khawarizmi Artificial Intelligence Program (Grant No. alkhawarizmi/2020/23).

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Authors and Affiliations

  1. Engineering Science Laboratory, FPT, Sidi Mohamed Ben Abdellah University, Fes, Morocco

    Karim El Moutaouakil

  2. LISAC Laboratory, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco

    Ali Yahyaouy

  3. MorphoSciences Research Laboratory, FMPM, UKAM Morocco, Fes, Morocco

    Saliha Chellak

  4. Biosciences and Health Laboratory, FMP, UKAM Morocco, Fes, Morocco

    Hicham Baizri

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  1. Karim El Moutaouakil
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Contributions

Corresponding authors: KEM. Data collection: AY. Theoretical part and processing: KEM. Data verification, results analysis, and diet recommendations: HB and SC. Redaction: KEM and AY.

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Correspondence to Karim El Moutaouakil.

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El Moutaouakil, K., Yahyaouy, A., Chellak, S. et al. An Optimized Gradient Dynamic-Neuro-Weighted-Fuzzy Clustering Method: Application in the Nutrition Field. Int. J. Fuzzy Syst. 24, 3731–3744 (2022). https://doi.org/10.1007/s40815-022-01358-0

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