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Neural Computing and Applications
Erschienen in: Neural Computing and Applications 9/2019

12.01.2019 | Original Article

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

verfasst von: Danilo Costarelli, Anna Rita Sambucini, Gianluca Vinti

Erschienen in: Neural Computing and Applications | Ausgabe 9/2019

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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 univariate and multivariate settings. In particular, the case of reconstruction and enhancement of biomedical (vascular) image has been discussed in detail.
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Nächster Artikel Three-operator splitting scheme with the reference image regularization for electrical capacitance tomography

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Literatur
1.
Adler A, Guardo R (1994) A neural network image reconstruction technique for electrical impedance tomography. IEEE Trans Med Imaging 13(4):594–600CrossRef
2.
Angeloni L, Costarelli D, Vinti G (2018) A characterization of the convergence in variation for the generalized sampling series. Annales Academiae Scientiarum Fennicae Mathematica 43:755–767MathSciNetMATHCrossRef
3.
Angeloni L, Vinti G (2009) Convergence and rate of approximation for linear integral operators in \(BV^\varphi \)-spaces in multidimensional setting. J Math Anal Appl 349:317–334MathSciNetMATH
4.
Angeloni L, Vinti G (2010) Approximation with respect to Goffman–Serrin variation by means of non-convolution type integral operators. Numer Funct Anal Optim 31:519–548MathSciNetMATHCrossRef
5.
Angeloni L, Vinti G (2014) Convergence and rate of approximation in BV\(\varphi ({\mathbb{R}}^N_+)\) for a class of Mellin integral operators. Atti Accad Naz Lincei Rend Lincei Mat Appl 25:217–232MathSciNetMATH
6.
Asdrubali F, Baldinelli G, Bianchi F, Costarelli D, Rotili A, Seracini M, Vinti G (2018) Detection of thermal bridges from thermographic images by means of image processing approximation algorithms. Appl Math Comput 317:160–171MathSciNetMATH
7.
Asdrubali F, Baldinelli G, Bianchi F, Costarelli D, Evangelisti L, Rotili A, Seracini M, Vinti G (2018) A model for the improvement of thermal bridges quantitative assessment by infrared thermography. Appl Energy 211:854–864MATHCrossRef
8.
Ball KR, Grant C, Mundy WR, Shafera TJ (2017) A multivariate extension of mutual information for growing neural networks. Neural Netw 95:29–43CrossRef
9.
Bardaro C, Karsli H, Vinti G (2011) Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems. Appl Anal 90(3–4):463–474MathSciNetMATHCrossRef
10.
Bardaro C, Musielak J, Vinti G (2003) Nonlinear integral operators and applications. Series in nonlinear analysis and applications 9. W. De Gruyter & Co., BerlinMATHCrossRef
11.
12.
13.
14.
Bono-Nuez A, Bernal-Ruíz C, Martín-del-Brío B, Pérez-Cebolla FJ, Martínez-Iturbe A (2017) Recipient size estimation for induction heating home appliances based on artificial neural networks. Neural Comput Appl 28(11):3197–3207CrossRef
15.
16.
17.
Cao F, Chen Z (2012) The construction and approximation of a class of neural networks operators with ramp functions. J Comput Anal Appl 14(1):101–112MathSciNetMATH
18.
Cao F, Liu B, Park DS (2013) Image classification based on effective extreme learning machine. Neurocomputing 102:90–97CrossRef
19.
20.
Coroianu L, Gal SG (2014) Saturation and inverse results for the Bernstein max-product operator. Period Math Hungar 69:126–133MathSciNetMATHCrossRef
21.
Coroianu L, Gal SG (2017) \(L^p\)-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejer kernel. J Integral Equ Appl 29(2):349–364MATH
22.
Costarelli D, Minotti AM, Vinti G (2017) Approximation of discontinuous signals by sampling Kantorovich series. J Math Anal Appl 450(2):1083–1103MathSciNetMATHCrossRef
23.
24.
25.
Costarelli D, Spigler R (2018) Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation. Comput Appl Math 37(1):99–133MathSciNetMATHCrossRef
26.
Costarelli D, Vinti G (2016) Approximation by max-product neural network operators of Kantorovich type. Results Math 69(3):505–519MathSciNetMATHCrossRef
27.
Costarelli D, Vinti G (2016) Max-product neural network and quasi-interpolation operators activated by sigmoidal functions. J Approx Theory 209:1–22MathSciNetMATHCrossRef
28.
Costarelli D, Vinti G (2016) Pointwise and uniform approximation by multivariate neural network operators of the max-product type. Neural Netw 81:81–90MATHCrossRef
29.
Costarelli D, Vinti G (2017) Saturation classes for max-product neural network operators activated by sigmoidal functions. Results Math 72(3):1555–1569MathSciNetMATHCrossRef
30.
Costarelli D, Vinti G (2017) Convergence for a family of neural network operators in Orlicz spaces. Mathematische Nachrichten 290(2–3):226–235MathSciNetMATHCrossRef
31.
Costarelli D, Vinti G (2017) Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting. Mathematica Slovaca 67(6):1469–1480MathSciNetMATHCrossRef
32.
33.
34.
Egmont-Petersena M, de Ridderb D, Handels H (2002) Image processing with neural networks—a review. Pattern Recognit 35:2279–2301MATHCrossRef
35.
36.
Gnecco G, Sanguineti M (2011) On a variational norm tailored to variable-basis approximation schemes. IEEE Trans Inf Theory 57:549–558MathSciNetMATHCrossRef
37.
Goh ATC (1995) Back-propagation neural networks for modeling complex systems. Artif Intell Eng 9:143–151CrossRef
38.
39.
Guliyev NJ, Ismailov VE (2018) On the approximation by single hidden layer feedforward neural networks with fixed weights. Neural Networks 98:296–304CrossRef
40.
Guliyev NJ, Ismailov VE (2018) Approximation capability of two hidden layer feedforward neural networks with fixed weights. Neurocomputing 316:262–269CrossRef
41.
42.
Kainen PC, Kurkova V, Sanguineti M (2009) Complexity of Gaussian-radial-basis networks approximating smooth functions. J Complex 25(1):63–74MathSciNetMATHCrossRef
43.
Lai G, Liu Z, Zhang Y, Philip Chen CL (2016) Adaptive position/attitude tracking control of aerial robot with unknown inertial matrix based on a new robust neural identifier. IEEE Trans Neural Netw Learn Syst 27(1):18–31MathSciNetCrossRef
44.
Liu P, Wang J, Zeng Z (2017) Multistability of delayed recurrent neural networks with Mexican hat activation functions. Neural Comput 29(2):423–457MathSciNetMATHCrossRef
45.
Livingstone DJ (2008) Artificial neural networks: methods and applications (methods in molecular biology). Humana Press, New York
46.
47.
Musielak J (1983) Orlicz spaces and modular spaces. Lecture notes in mathematics, vol 1034. Springer, BerlinMATHCrossRef
48.
49.
Olivera JJ (2017) Global exponential stability of nonautonomous neural network models with unbounded delays. Neural Netw 96:71–79CrossRef
50.
Rister B, Rubin DL (2017) Piecewise convexity of artificial neural networks. Neural Netw 94:34–45CrossRef
51.
Sahoo A, Xu H, Jagannathan S (2016) Adaptive neural network-based event-triggered control of single-input single-output nonlinear discrete-time systems. IEEE Trans Neural Netw Learn Syst 27(1):151–164MathSciNetCrossRef
52.
Stamov G, Stamova I (2017) Impulsive fractional-order neural networks with time-varying delays: almost periodic solutions. Neural Comput Appl 28(11):3307–3316CrossRef
Metadaten
Titel
Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications
verfasst von
Danilo Costarelli
Anna Rita Sambucini
Gianluca Vinti
Publikationsdatum
12.01.2019
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 9/2019
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-018-03998-6

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