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Elastic-Net Regression based on Empirical Mode Decomposition for Multivariate Predictors

Abdullah Suleiman Al-Jawarneh and Mohd. Tahir Ismail

Pertanika Journal of Science & Technology, Volume 29, Issue 1, January 2021

DOI: https://doi.org/10.47836/pjst.29.1.11

Published: 22 January 2021

The empirical mode decomposition (EMD) method is used to decompose the non-stationary and nonlinear signal into a finite set of orthogonal non-overlapping time scale components that include several intrinsic mode function components and one residual component. Elastic net (ELN) regression is a statistical penalized method used to address multicollinearity among predictor variables and identify the necessary variables that have the most effect on the response variable. This study proposed the use of the ELN method based on the EMD algorithm to identify the decomposition components of multivariate predictor variables with the most effect on the response variable under multicollinearity problems. The results of the numerical experiments and real data confirmed that the EMD-ELN method is highly capable of identifying the decomposition components with the presence or absence of multicollinearity among the components. The proposed method also achieved the best estimation and reached the optimal balance between the variance and bias. The EMD-ELN method also improved the accuracy of regression modeling compared with the traditional regression models.

  • Al-Jawarneh, A. S., Ismail, M. T., Awajan, A. M., & Alsayed, A. R. (2020). Improving accuracy models using elastic net regression approach based on empirical mode decomposition. Communications in Statistics-Simulation and Computation, 2020, 1-20. doi: https://doi.org/10.1080/03610918.2020.1728319

  • Chu, H., Wei, J., & Qiu, J. (2018). Monthly streamflow forecasting using EEMD-Lasso-DBN method based on multi-scale predictors selection. Water, 10(10), 1-15. doi: https://doi.org/10.3390/w10101486

  • Chui, C. (1995). Wavelet basics. Boston, Massachusetts: Kulwer Academic Publishers.

  • Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1-22.

  • Hamid, H., Ngu, P., & Alipiah, F. (2018). New smoothed location models integrated with PCA and two types of MCA for handling large number of mixed continuous and binary variables. Pertanika Journal of Science and Technology, 26(1), 247-260.

  • Hashibah, H., & Mahat, N. I. (2013). Using principal component analysis to extract mixed variables for smoothed location model. Far East Journal of Mathematical Sciences, 80(1), 33-54.

  • Haws, D. C., Rish, I., Teyssedre, S., He, D., Lozano, A. C., Kambadur, P., … & Parida, L. (2015). Variable-selection emerges on top in empirical comparison of whole-genome complex-trait prediction methods. PloS One, 10(10), 1-22. doi: 10.1371/journal.pone.0138903

  • Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

  • Huang, N. E. (2014). Introduction to the Hilbert–Huang transform and its related mathematical problems. In Hilbert–Huang transform and its applications (pp. 1-26). Singapore: World Scientific. doi: https://doi.org/10.1142/9789814508247_0001

  • Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., ... & Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1971), 903-995. doi: https://doi.org/10.1098/rspa.1998.0193

  • Jadhav, N. H., Kashid, D. N., & Kulkarni, S. R. (2014). Subset selection in multiple linear regression in the presence of outlier and multicollinearity. Statistical Methodology, 19, 44-59. doi: https://doi.org/10.1016/j.stamet.2014.02.002

  • Javaid, A., Ismail, M., & Ali, M. K. M. (2020). Efficient model selection of collector efficiency in solar dryer using hybrid of LASSO and robust regression. Pertanika Journal of Science and Technology, 28(1), 193-210.

  • Masselot, P., Chebana, F., Bélanger, D., St-Hilaire, A., Abdous, B., Gosselin, P., & Ouarda, T. B. (2018). EMD-regression for modelling multi-scale relationships, and application to weather-related cardiovascular mortality. Science of The Total Environment, 612, 1018-1029. doi: https://doi.org/10.1016/j.scitotenv.2017.08.276

  • Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to linear regression analysis (Vol. 821). Hoboken, New Jersey: John Wiley & Sons.

  • Naik, J., Satapathy, P., & Dash, P. (2018). Short-term wind speed and wind power prediction using hybrid empirical mode decomposition and kernel ridge regression. Applied Soft Computing, 70(1), 1167-1188. doi: https://doi.org/10.1016/j.asoc.2017.12.010

  • Qin, L., Ma, S., Lin, J. C., & Shia, B. C. (2016). Lasso regression based on empirical mode decomposition. Communications in Statistics-Simulation and Computation, 45(4), 1281-1294. doi: https://doi.org/10.1080/03610918.2013.826361

  • Shen, Z., Feng, N., & Shen, Y. (2012). Ridge regression model-based ensemble empirical mode decomposition for ultrasound clutter rejection. Advances in Adaptive Data Analysis, 4(1-2), 1-7. doi: https://doi.org/10.1142/S1793536912500136

  • Shen, Z., & Lee, C. H. (2012, March 25-30). A lasso based ensemble empirical mode decomposition approach to designing adaptive clutter suppression filters. In 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 757-760). Kyoto, Japan.

  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288. doi: https://doi.org/10.1111/j.2517-6161.1996.tb02080.x

  • Titchmarsh, E. C. (1948). Introduction to the theory of fourier integrals (Vol. 950). Oxford, UK: Clarendon Press.

  • Yan, X., & Su, X. (2009). Linear regression analysis: Theory and computing. Singapore: World Scientific.

  • Yang, A. C., Fuh, J. L., Huang, N. E., Shia, B. C., Peng, C. K., & Wang, S. J. (2011). Temporal associations between weather and headache: Analysis by empirical mode decomposition. PloS One, 6(1), 1-6. doi: https://doi.org/10.1371/journal.pone.0014612

  • Zhou, D. X. (2013). On grouping effect of elastic net. Statistics and Probability Letters, 83(9), 2108-2112. doi: https://doi.org/10.1016/j.spl.2013.05.014

  • Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301-320. doi: https://doi.org/10.1111/j.1467-9868.2005.00503.x