Training of recurrent neural networks using the embedding dimension in the space the phases

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Nelly Patricia Perugachi Cahueñas
Mariela Micaela Moreno Palacios
Arquímides Xavier Haro Velasteguí

Abstract

A method is proposed using Recurrent Neural Networks for the prediction of chaotic data, applying Chaos Theory, to study the dynamic behavior of the data in the multidimensional space of the phases, establish the correlation of the same and determine the embedding dimensions as a basis for the training of the neural networks, as well as determine the dynamic characteristics of the system by calculating the Lyapunov coefficients and the Kolmorov-Siani entropy,  that tell us the degree of disorder that the system has, to project the accuracy of the prediction. Data on PM2.5 pollutants taken in the Historic Center of the city of Quito, at one-hour intervals, between the years 2005 to 2019, are used. The results determine that the data series correspond to a chaotic system (more than one positive Lyapunov coefficient), so the application of Chaos Theory in the analysis of them is justified, giving good results in the predictions applying the methods of recurrent neural networks of Elman and Jordan, when comparing the predicted series they are shown that they do not present significant differences between them,   nor with the measured data, using the method of variance with 0.05 significance, the percentage square error with respect to the range of variation of the data is approximately 5% in both cases. Objectives: To propose a method that helps the training of neural networks using Chaos Theory, by implementing the socket dimension in the space of the phases.

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Perugachi Cahueñas, N. P., Moreno Palacios, M. M., & Haro Velasteguí, A. X. (2022). Training of recurrent neural networks using the embedding dimension in the space the phases. ConcienciaDigital, 5(3.1), 254-274. https://doi.org/10.33262/concienciadigital.v5i3.1.2252
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