Stochastic One-Step Training for Feedforward Artificial Neural Networks
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Stochastic One-Step Training for Feedforward Artificial Neural Networks Hector Cano-Rocha1
· Raul Gonzalez-Garcia1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper studies the use and application of a fast method (non-iterative and instantaneous) for Feedforward Neural Networks training in which the weights of the hidden layer are assigned randomly, and the weights of the output layer are trained through a linear regression adjustment. The method solves two of the problems that are present in traditional training: training time and optimal structure. While traditional iterative training methods require long periods to train a single structure, the proposed method allows training a structure in a single step (not iterative). In this way, by scanning the number of neurons in the hidden layer, many structures are trained in a short time, and it is possible to obtain an optimal topology. A quality control criterion of the predictions is proposed based on the coefficient of determination that guarantees short times and an optimal number of hidden neurons to characterize a specific problem. The feasibility of the proposed method is tested by comparing its performance against building functions of the artificial neural networks toolbox in Matlab® , resulting superior in both approximation quality and training time. A rigorous study and analysis are performed for the regression of simulated data on two different surfaces with a specific noise and different topologies of the neural network. The resulting process time is at least 150 times shorter for proposed training than with the iterative training that Matlab uses, thus obtaining well-founded learning rules. A novel way of an amputated matrix is proposed that breaks the paradigm of the way multiple-output systems are trained and improves the quality of predictions with no detriment to training times. Keywords Feedforward neural network · Constructive networks · Training · Cross-validation · Single-hidden layer feedforward network · Multiple responses
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Raul Gonzalez-Garcia [email protected] Hector Cano-Rocha [email protected]
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Facultad de Ciencias Químicas, Universidad Autónoma de San Luis Potosí, Av. Dr. Manuel Nava No. 6, 78210 San Luis Potosí, Mexico
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H. Cano-Rocha, R. Gonzalez-Garcia
1 Introduction Modeling the behavior of a system is of vital importance for its study, analysis, control, and optimization. The main objective of modeling is to find a function capable of providing a good approximation to the system’s experimental data, in addition to filtering experimental noise. An alternative for the modeling of a system is models based on neural networks. To training these models, it is necessary to have a large amount of data of the system, besides exist two problems that are present in traditional training: training time and optimal structure. Where training time is usually large due to the algorithms of optimization are slow and require long periods to train a single structure. We proposed a train
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