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

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.

19 pages

References in corpus (5)

• On the approximation by single hidden layer feedforward neural networks with fixed weights
• Approximation capability of two hidden layer feedforward neural networks with fixed weights
• Approximation results in Orlicz spaces for sequences of Kantorovich max-product neural network operators
• Filter convergence and decompositions for vector lattice-valued measures
• $L^p$ spaces in vector lattices and applications

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• Abstract integration with respect to measures and applications to modular convergence in vector lattice setting
• Simultaneous approximation by neural network operators with applications to Voronovskaja formulas
• Max-product Kantorovich sampling operators: quantitative estimates in functional spaces
• Some applications of modular convergence in vector lattice setting