22. Electrocardiogram time series forecasting and optimization using ant colony optimization algorithm

Paulius Čepulionis1, Kristina Lukoševičiūtė2

Kaunas University of Technology, Kaunas, Lithuania

1Corresponding author

E-mail: 1paulius.cepulionis@ktu.edu, 2kristina.lukoseviciute@ktu.lt

(Received 30 April 2016; accepted 2 June 2016)

Abstract. The aim of this work is to create the time series dynamic model, which is based on non‑uniform embedding in the phase-space. To solve selection of time delays problem efficiently, this paper proposes an ant colony optimization (ACO) way. Firstly, false nearest neighbor method is used for determine the embedding dimension. Secondly, ant colony optimization algorithm is used for non-uniform time delay search. To quicken search speed, roulette wheel selection algorithm distributes ants’ pheromones. Optimization fitness function is the average area of all attractors. Obtained embeddings found by this model are applied in time-series forecasting using radial basis function neural networks. The study is presented in Mackey-Glass and electrocardiogram (ECG) time series forecasting. Prediction results show that the proposed model provides precise prediction accuracy.

Keywords: non-uniform embedding, ant colony optimization, electrocardiogram, time series forecasting.


[1]        Shen M., Chen W.-N., Zhang J., Chung H. S.-H., Kaynak O. Optimal selection of parameters for nonuniform embedding of chaotic time series using ant colony optimization. Cybernetics, Vol. 43, Issue 2, 2013, p. 790‑802.

[2]        Zhang J., Chung S.-H., Lo W-L. Chaotic time series prediction using a neuro-fuzzy system with time‑delay coordinates. Knowledge and Data Engineering, Vol. 20, Issue 7, 2008, p. 956‑964.

[3]        Brockwell P. J., Davis R. A. Introduction to Time Series and Forecasting. Springer Science and Business Media, 2006.

[4]        Pecora L. M., Moniz L., Nichols J., Carrol T. L. A unified approach to attractor reconstruction. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 17, Issue 1, 2007, p. 013110.

[5]        Su L. Y. Prediction of multivariate chaotic time series with local polynomial fitting. Computers and Mathematics with Applications, Vol. 59, Issue 2, 2010, p. 737‑744.

[6]        Moody G., Goldberger A., McClennen S., Swiryn S. Predicting the onset of paroxysmal atrial fibrillation: the computers in cardiology challenge 2001. Computers in Cardiology, Vol. 28, Issue 1, 2001, p. 113‑116.

[7]        Tang X. Novel Remote ECG Real-Time Monitoring System. M.Phil. Thesis, Hong Kong University of Science and Technology, 2009.

[8]        Rhodes C., Morari M. False-nearest-neighbors algorithm and noise-corrupted time series. Physical Review, Vol. 55, Issue 5, 1997, p. 6162‑6170.

[9]        Mezeiová K., Krakovská A. Choice of measurement for phase-space reconstruction: decision based on false nearest neighbors method. Journal of Complex Systems, 2011, p. 55‑58.

[10]     Zhao F., Dong J., Li S., Sun J. An improved ant colony optimization algorithm with embedded genetic algorithm for the traveling salesman problem. Intelligent Control and Automation, 2008, p. 7902‑7906.

[11]     Al-Qaheri H. Digital watermarking using ant colony optimization in fractional Fourier domain. Journal of Information Hiding and Multimedia Signal Processing, Vol. 1, Issue 3, 2010, p. 179‑189.

[12]     Arabas J., Bartnik L., Opara K. DMEA – an algorithm that combines differential mutation with the fitness proportionate selection. Differential Evolution (SDE), 2011, p. 1‑8.

[13]     Lukoseviciute K., Ragulskis M. Evolutionary algorithms for the selection of time lags for time series forecasting by fuzzy inference systems. Neurocomputing, Vol. 73, Issue 10, 2010, p. 2077‑2088.

[14]     Packard N. H., Crutch J. P., Farmer J., Shaw R. Geometry from a time series. Physical Review Letters, Vol. 45, 1980, p. 712‑716.

[15]     Ma N., Lu C., Zhang W. J., Wu X. H. Application of parallel RBF network on iterative prediction of chaotic time series. Chaos-Fractals Theories and Applications (IWCFTA), 2010, p. 341‑345.

[16]     Haiping D., Nong Z. Time series prediction using evolving radial basis function networks with new encoding scheme. Neurocomputing, Vol. 71, Issues 7‑9, 2008, p. 1388‑1400.

[17]     Bouaziz S., Alimi A. M., Abraham A. PSO-based update memory for improved harmony search algorithm to the evolution of FBBFNT’ parameters. Evolutionary Computation (CEC), 2014, p. 1951‑1958.

[18]     Bouaziz S., Dhahri H., Alimi A. M., Abraham A. Evolving flexible beta basis function neural tree using extended genetic programming and hybrid artificial bee colony. Applied Soft Computing, 2016, p. 1‑16.

[19]     Bouaziz S., Alimi A. M., Abraham A. Evolving flexible beta basis function neural tree for nonlinear systems. Neural Networks (IJCNN), 2013, p. 1‑8.

[20]     Jaddi N. S., Abdullah S., Hamdan A. R. A solution representation of genetic algorithm for neural network weights and structure. Information Processing Letters, Vol. 116, Issue 1, 2016, p. 22‑25.

[21]     Chen Y., Yang B., Dong J., Abraham A. Time-series forecasting using flexible neural tree model. Information Sciences, Vol. 174, Issue 3, 2005, p. 219‑235.

[22]     Chen Y., Yang B., Dong J. Nonlinear system modelling via optimal design of neural trees. International Journal of Neural Systems, Vol. 14, Issue 2, 2004, p. 125‑137.

[23]     Kim J., Kasabov N. HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Networks, Vol. 12, Issue 9, 1999, p. 1301‑1319.

[24]     Cho K. B., Wang B. H. Radial basis function based adaptive fuzzy systems their application to system identification and prediction. Fuzzy Sets and Systems, Vol. 83, 1995, p. 325‑339.

[25]     Qin Z., Tang Y. Uncertainty Modeling for Data Mining: A Label Semantics Approach. Springer, 2014.

[26]     Kasabov N. K., Kim J., Watts M. J., Gray A. R. FuNN/2 – a fuzzy neural network architecture for adaptive learning and knowledge acquisition. Information Sciences, Vol. 101, Issue 3, 1997, p. 155‑175.

[27]     Lee S. H., Kim I. T. Time series analysis using fuzzy learning. ICONIP: International Conference on Neural Information Processing, Vol. 3, Issue 3, 1994, p. 1577‑1582.

[28]     Lazzús J. A., Salfate I., Montecinos S. Hybrid neural network-particle swarm algorithm to describe chaotic time series. Neural Network World, Vol. 24, Issue 6, 2014, p. 601‑617.

[29]     Box G. E. P., Jenkins G. M. Time Series Analysis: Forecasting and Control. Holdenday, San Francisco, Vol. 22, Issue 2, 1976, p. 199‑201.

Cite this article

Čepulionis Paulius, Lukoševičiūtė Kristina Electrocardiogram time series forecasting and optimization using ant colony optimization algorithm. Mathematical Models in Engineering, Vol. 2, Issue 1, 2016, p. 69‑77.


Mathematical Models in Engineering. June 2016, Volume 2, Issue 1

© JVE International Ltd. ISSN Print 2351-5279, ISSN Online 2424-4627, Kaunas, Lithuania