Abstract
This study considers sufficient and also necessary conditions for the universal approximation capability of three-layer feedforward generalized Mellin approximate identity neural networks. Our approach consists of three steps. In the first step, we introduce a notion of generalized Mellin approximate identity. In the second step, we prove a theorem by using this notion to show convolution linear operators of generalized Mellin approximate identity with a continuous function f on \( {\mathbb{R}}^{+} \) with a compact support converges uniformly to f. In the third step, we establish a main theorem by using those previous steps. The theorem shows universal approximation by generalized Mellin approximate identity neural networks.
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References
Huang GB, Chen L, Siew CK. Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw. 2006;17(4):879–99.
Ismailov VE. Approximation by neural networks with weights varying on a finite set of directions. J Math Anal Appl. 2012;389(1):72–83.
Costarelli D. Interpolation by neural network operators activated by ramp functions. J Math Anal Appl. 2014;419(1):574–82.
Arteaga C, Marrero M. Universal approximation by radial basis function networks of Delsarte translates. Neural Netw. 2013;46(10):299–305.
Yu DS. Approximation by neural networks with sigmoidal functions. Acta Math Sin Engl Ser. 2013;29(10):2013–26.
Ismailov VE. On the approximation by neural networks with bounded number of neurons in hidden layers. J Math Anal Appl. 2014;417(2):963–69.
Turchetti C, Conti M, Crippa P, Orcioni S. On the approximation of stochastic processes by approximate identity neural networks. IEEE Trans Neural Netw. 1998;9(6):1069–85.
Panahian Fard S, Zainuddin Z. Analyses for L p[a, b]-norm approximation capability of flexible approximate identity neural networks. Neural Comput Appl. 2013;24(1):45–50.
Panahian Fard S, Zainuddin Z. On the universal approximation capability of flexible approximate identity neural networks. Lect Notes Electrical Eng I. 2013;236:201–7.
Zainuddin Z, Panahian Fard S. Double approximate identity neural networks universal approximation in real Lebesgue spaces. Lect Notes Comput Sci I. 2012;7663:409–15.
Panahian Fard S, Zainuddin Z. The universal approximation capability of double flexible approximate identity neural networks. Lect Notes Electrical Eng. 2014;277:125–33.
Panahian Fard S, Zainuddin Z. The universal approximation capabilities of 2π-periodic approximate identity neural networks. The International Conference on Information Science and Cloud Computing; 2013 Dec 7–8; Guangzhou, China; IEEE; 2013.
Panahian Fard S, Zainuddin Z: The universal approximation capabilities of Mellin approximate identity neural networks. Lect Notes Comput Sci I. 2013;7951:205–13.
Wu W, Nan D, Li Z, Long J. Approximation to compact set of functions by feedforward neural networks. In 20th International Joint Conference on Neural Networks; Orlando, FL; 2007. pp. 1222–5.
Singh B, Sharma K, Rathi S, Singh G. A generalized log-normal distribution and its goodness of fit to censored data. Comput Stat. 2012;27(1):51–67.
Panahian Fard S, Zainuddin Z. The universal approximation capabilities of double 2Ï€-periodic approximate identity neural networks. Soft Comput. 2014; DOI 10.1007/s00500-014-1449-8
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Panahian Fard, S., Zainuddin, Z. (2015). Universal Approximation by Generalized Mellin Approximate Identity Neural Networks. In: Wong, W. (eds) Proceedings of the 4th International Conference on Computer Engineering and Networks. Lecture Notes in Electrical Engineering, vol 355. Springer, Cham. https://doi.org/10.1007/978-3-319-11104-9_22
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DOI: https://doi.org/10.1007/978-3-319-11104-9_22
Publisher Name: Springer, Cham
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