Training of recurrent neural networks using the embedding dimension in the space the phases
Article Sidebar
Main Article Content
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.
Downloads
Article Details
References
Bochi, J., & Rams, M. (2016). The entropy of Lyapunov-optimizing measures of some matrix cocycles. Journal of Modern Dynamics, 10, 255–286. https://doi.org/10.3934/jmd.2016.10.255
Cruz, B., Martínez, S., Abed, R., Ábalo, G., Lorenzo, G., Matilde, M., & Lorenzo, M. G. (2007). Redes neuronales recurrentes para el análisis de secuencias Recurrente neurales / network for sequences analysis. Rcci, 1, 11.
Díaz, M. (2016). Redes neuronales recurrentes y series temporales. http://software-tecnico-libre.es/es/articulo-por-tema/todas-las-secciones/todos-los-temas/todos-los-articulos/redes-neuronales-recurrentes-y-series-de-tiempo
Domański, P. D., & Ławryńczuk, M. (2017). Assessment of predictive control performance using fractal measures. Nonlinear Dynamics, 89(2), 773–790. https://doi.org/10.1007/s11071-017-3484-3
Fernández, D. G. (2014). Reducción del ruido y predicción de series temporales de alta frecuencia mediante sistemas dinámicos no lineales y técnicas neurales. Banco Central Del Uruguay, (1688), 15. http://www.bcu.gub.uy/Estadisticas-e-Indicadores/Documentos de Trabajo/1.2014.pdf
Fowler, Andrew., & McGuinness, M. (2010). Chaos: An Introduction for Applied Mathematicians. (S. Nature, Ed.). New Zeland. https://books.google.com.ec/books?hl=es&lr=&id=SdzODwAAQBAJ&oi=fnd&pg=PR8&dq=Chaos+An+Introduction+for+Applied+Mathematicians,+Switzerland,+Springer&ots=rqAReTU6eR&sig=TPdrthtsZG9OCH0j--37iAzdPIc#v=onepage&q=Chaos An Introduction for Applied Mathematician
Géron, A. (2017). Hands-On Machine Learning with Scikit-Learn & TensorFlow. https://www.oreilly.com/library/view/hands-on-machine-learning/9781491962282/
González, J. C., Tudurí, J. M., & Rul-lan, G. (2017). Análisis de Series Temporales Usando Redes Neuronales Recurrentes. https://www.apsl.net/blog/2017/06/14/analisis-de-series-temporales-usando-redes-neuronales-recurrentes/
Hegger, R., Kantz, H., & Schreiber, T. (1999). Practical implementation of nonlinear time series methods: The TISEAN package. Chaos, 9(2), 413–435. https://doi.org/10.1063/1.166424
Ivancevic, V. G., & Ivancevic, T. T. (2007). Introduction to Attractors and Chaos. In High-Dimensional Chaotic and Attractor Systems (pp. 1–151). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-1-4020-5456-3_1
Kocak, C., Dalar, A. Z., Cagcag Yolcu, O., Bas, E., & Egrioglu, E. (2020). A new fuzzy time series method based on an ARMA-type recurrent Pi-Sigma artificial neural network. Soft Computing, 24(11), 8243–8252. https://doi.org/10.1007/s00500-019-04506-1
Lewis, N. (2016). Deep time series forecasting with phyton. (C. I. P. Platform, Ed.). Retrieved from https://www.goodreads.com/book/show/33843624-deep-time-series-forecasting-with-python
Li, X., Peng, L., Yao, X., Cui, S., Hu, Y., You, C., & Chi, T. (2017). Long short-term memory neural network for air pollutant concentration predictions: Method development and evaluation. Environmental Pollution, 231, 997–1004. https://doi.org/10.1016/j.envpol.2017.08.114
López, Jesús., & Caicedo, E. (2009). Una aproximación práctica a las Redes Neuronales Artificiales. (P. E. U. del Valle, Ed.) (Primera). Universidad del Valle. https://www.researchgate.net/publication/303365431_Una_aproximacion_practica_a_las_Redes_Neuronales_Artificiales
Medvinsky, A. B., Nurieva, N. I., Rusakov, A. V., & Adamovich, B. V. (2017). Deterministic chaos and the problem of predictability in population dynamics. Biophysics (Russian Federation), 62(1), 92–108. https://doi.org/10.1134/S0006350917010122
Motter, A. E., & Campbell, D. K. (2013). Chaos at fifty. Physics Today, 66(5), 27–33. https://doi.org/10.1063/PT.3.1977
Pino-Vallejo, M., Tierra, A., Haro, A., & Perugachi, N. (2018). Prediction of concentrations of PM2.5 in downtown Quito using the chaos theory. AIP Conference Proceedings, 2003, 1–8. https://doi.org/10.1063/1.5050365
Rebala, G., Ravi, A., & Churiwala, S. (2019). An Introduction to Machine Learning. (Springer International Publishing, Ed.). l. https://books.google.com.ec/books/about/An_Introduction_to_Machine_Learning.html?id=gckwygEACAAJ&redir_esc=y
Rodríguez, A. (2015). Contaminación atmosférica y justicia ambiental en Quito. FLACSO. https://repositorio.flacsoandes.edu.ec/xmlui/handle/10469/8549
Stolz, I., & Keller, K. (2017). A general symbolic approach to Kolmogorov-Sinai entropy. Entropy, 19(12), 1–19. https://doi.org/10.3390/e19120675
Valentin, A. (2009). Y bolotin a tur, V. Yanovsky, chaos, concept, control and consnhuctive Use. (Caron, Ed.) (Springer C). Springer. https://www.researchgate.net/publication/281089929_YBolotinATurVYanovskyChaosConceptcontrol_and_Consnhuctive_UseSpringerISBN_978-3-642-00936-5
Zhou, S., Li, W., & Qiao, J. (2017). Prediction of PM2.5 concentration based on recurrent fuzzy neural network. Chinese Control Conference, CCC, 3920–3924. https://doi.org/10.23919/ChiCC.2017.8027970