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arXiv · 1812.11543

Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications

Danilo Costarelli·Anna Rita Sambucini·Gianluca Vinti
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Abstract

In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in the general frame of the Orlicz spaces, which includes as particular case the $L^p$-spaces. Examples of sigmoidal activation functions are discussed, for the above operators in different cases of Orlicz spaces. Finally, concrete applications to real world cases have been presented in both uni-variate and multivariate settings. In particular, the case of reconstruction and enhancement of biomedical (vascular) image has been discussed in details.

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Danilo Costarelli, Anna Rita Sambucini, Gianluca Vinti. 2018-12-30. Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications. https://doi.org/10.1007/s00521-018-03998-6

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