Density-based unsupervised ensemble learning methods for time series forecasting of aggregated or clustered electricity consumption

  • Peter LaurinecEmail author
  • Marek Lóderer
  • Mária Lucká
  • Viera Rozinajová


This paper presents a comparison of the impact of various unsupervised ensemble learning methods on electricity load forecasting. The electricity load from consumers is simply aggregated or optimally clustered to more predictable groups by cluster analysis. The clustering approach consists of efficient preprocessing of data obtained from smart meters by a model-based representation and the K-means method. We have implemented two types of unsupervised ensemble learning methods to investigate the performance of forecasting on clustered or simply aggregated load: bootstrap aggregating based and the newly proposed density-clustering based. Three new bootstrapping methods for time series analysis methods were newly proposed in order to handle the noisy behaviour of time series. The smart meter datasets used in our experiments come from Australia, London, and Ireland, where data from residential consumers were available. The achieved results suggest that for extremely fluctuating and noisy time series the forecasting accuracy improvement through the bagging can be a challenging task. However, our experimental evaluation shows that in most of the cases the density-based unsupervised ensemble learning methods are significantly improving forecasting accuracy of aggregated or clustered electricity load.


Forecasting Bagging Clustering Unsupervised learning Ensemble learning 



This work was supported by Slovak Research and Development Agency under the contract No. APVV-16-0484 and No. APVV-16-0213, as well as with the support of the Research and Development Operational Programme for the project International centre of excellence for research of intelligent and secure information-communication technologies and systems, ITMS 26240120039, co-funded by the ERDF.


  1. Adhikari, R., Verma, G., Khandelwal, I. (2015). A model ranking based selective ensemble approach for time series forecasting. Procedia Computer Science, 48, 14–21.CrossRefGoogle Scholar
  2. Ankerst, M., Breunig, M.M., Kriegel, H.P., Sander, J. (1999). Optics: ordering points to identify the clustering structure. In ACM Sigmod record (Vol. 28, pp. 49–60). ACM.Google Scholar
  3. Arthur, D., & Vassilvitskii, S. (2007). K-means++: the advantages of careful seeding. In SODA ’07 Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms (pp. 1027–1035).Google Scholar
  4. Bartholomew, D.J., Box, G.EP., Jenkins, G.M. (1971). Time series analysis forecasting and control. Operational Research Quarterly (1970–1977), 22(2), 199. Scholar
  5. Bergmeir, C., Hyndman, R.J., Benítez, JM. (2016). Bagging exponential smoothing methods using stl decomposition and box–cox transformation. International Journal of Forecasting, 32(2), 303–312.CrossRefGoogle Scholar
  6. Bilton, M., Carmichael, R., Schofield, J.R., Strbac, G., Tindemans, S.,Woolf, M. (2016). Low carbon london project: data from the dynamic time-of-use electricity pricing trial, 2013. [data collection]. UK Data Service. SN: 7857,
  7. Bouktif, S., Fiaz, A., Ouni, A., Serhani, M.A. (2018). Optimal deep learning LSTM model for electric load forecasting using feature selection and genetic algorithm: comparison with machine learning approaches. Energies, 11(7).
  8. Breiman, L. (1996). Bagging predictors. Machine Learning, 24(2), 123–140. Scholar
  9. Breiman, L., Friedman, J., Stone, C.J., Olshen, R.A. (1984). Classification and regression trees. Boca Raton: CRC Press.zbMATHGoogle Scholar
  10. Ceci, M., Corizzo, R., Fumarola, F., Malerba, D., Rashkovska, A. (2017). Predictive modeling of pv energy production: how to set up the learning task for a better prediction? IEEE Transactions on Industrial Informatics, 13(3), 956–966. Scholar
  11. Cerqueira, V., Torgo, L., Pinto, F., Soares, C. (2017). Arbitrated ensemble for time series forecasting. In M. Ceci, J. Hollmén, L. Todorovski, C. Vens, S. Džeroski (Eds.) , Machine learning and knowledge discovery in databases (pp. 478–494). Cham: Springer International Publishing.Google Scholar
  12. Cleveland, R.B., Cleveland, W.S., McRae, J.E., Terpenning, I. (1990). STL: a seasonal-trend decomposition procedure based on Loess. Journal of Official Statistics, 6(1), 3–73.Google Scholar
  13. Davies, D.L., & Bouldin, DW. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1(2), 224–227. Scholar
  14. Ester, M., Kriegel, H.P., Sander, J., Xu, X., et al. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In Kdd (Vol. 96, pp. 226–231).Google Scholar
  15. Friedman, J., Hastie, T., Tibshirani, R. (2001). The elements of statistical learning, vol 1. Springer series in statistics, New York.Google Scholar
  16. Hamerly, G., & Elkan, C. (2004). Learning the k in k-means. In Advances in neural information processing systems (pp. 281–288).Google Scholar
  17. Holt, C.C. (2004). Forecasting seasonals and trends by exponentially weighted moving averages. International Journal of Forecasting, 20(1), 5–10.CrossRefGoogle Scholar
  18. Hyndman, R., & Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for r. Journal of Statistical Software, Articles, 27(3), 1–22. Scholar
  19. Hyndman, R.J., & Koehler, AB. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688.CrossRefGoogle Scholar
  20. Hyndman, R.J., Koehler, A.B., Snyder, R.D., Grose, S. (2002). A state space framework for automatic forecasting using exponential smoothing methods. International Journal of Forecasting, 18(3), 439–454. Scholar
  21. Keogh, E., Chakrabarti, K., Pazzani, M., Mehrotra, S. (2001). Dimensionality reduction for fast similarity search in large time series databases. Knowledge and information Systems, 3(3), 263–286.CrossRefzbMATHGoogle Scholar
  22. Kosková, G, Laurinec, P, Rozinajová, V, Ezzeddine, AB, Lucká, M, Lacko, P, Vrablecová, P, Návrat, P. (2015). Incremental ensemble learning for electricity load forecasting. Acta Polytechnica Hungarica, 13(2), 97–117.Google Scholar
  23. Kunsch, H.R. (1989). The jackknife and the bootstrap for general stationary observations. Annals of Statistics, 17(3), 1217–1241. Scholar
  24. Laurinec, P. (2018). Tsrepr r package: time series representations. Journal of Open Source Software, 3(23), 577. Scholar
  25. Laurinec, P, & Lucká, M. (2016). Comparison of representations of time series for clustering smart meter data. In Lecture notes in engineering and computer science: proceedings of the world congress on engineering and computer science (pp. 458–463).Google Scholar
  26. Laurinec, P, & Lucká, M. (2018a). Clustering-based forecasting method for individual consumers electricity load using time series representations. Open Computer Science, 8(1), 38–50.Google Scholar
  27. Laurinec, P, & Lucká, M. (2018b). Usefulness of unsupervised ensemble learning methods for time series forecasting of aggregated or clustered load. In A. Appice, C. Loglisci, G. Manco, E. Masciari, Z.W. Ras (Eds.) , New frontiers in mining complex patterns (pp. 122–137). Cham: Springer International Publishing.Google Scholar
  28. Laurinec, P, Lóderer, M, Vrablecová, P, Lucká, M, Rozinajová, V, Ezzeddine, AB. (2016). Adaptive time series forecasting of energy consumption using optimized cluster analysis. In 2016 IEEE 16th international conference on data mining workshops (ICDMW) (pp. 398–405). IEEE.Google Scholar
  29. Petropoulos, F, Hyndman, RJ, Bergmeir, C. (2018). Exploring the sources of uncertainty: why does bagging for time series forecasting work? European Journal of Operational Research, 268(2), 545–554. Scholar
  30. Pravilovic, S, Bilancia, M, Appice, A, Malerba, D. (2017). Using multiple time series analysis for geosensor data forecasting. Information Sciences, 380, 31–52.CrossRefGoogle Scholar
  31. Rendon, J, & de Menezes, LM. (2016). Structural combination of neural network models. In 2016 IEEE 16th international conference on data mining workshops (ICDMW) (pp. 406–413), DOI, (to appear in print).
  32. Shahzadeh, A., Khosravi, A, Nahavandi, S. (2015). Improving load forecast accuracy by clustering consumers using smart meter data. In 2015 international joint conference on neural networks (IJCNN). 1–7). IEEE.
  33. Shen, W., Babushkin, V., Aung, Z.,Woon,W.L. (2013). An ensemble model for day-ahead electricity demand time series forecasting. In Proceedings of the fourth international conference on future energy systems (pp. 51–62). ACM.Google Scholar
  34. Smiti, A, & Elouedi, Z. (2012). Dbscan-gm: an improved clustering method based on gaussian means and dbscan techniques. In 2012 IEEE 16th international conference on intelligent engineering systems (INES) (pp. 573–578). IEEE.Google Scholar
  35. Strasser, H, & Weber, C. (1999). On the asymptotic theory of permutation statistics. SFB Adaptive Information Systems and Modelling in Economics and Management Science.Google Scholar
  36. Wijaya, T.K., Vasirani, M., Humeau, S., Aberer, K. (2015). Cluster-based aggregate forecasting for residential electricity demand using smart meter data. In 2015 IEEE international conference on Big data (Big data). (pp. 879–887). IEEE.
  37. Xia, L., & Jing, J. (2007). An ensemble density-based clustering method. In International conference on intelligent systems and knowledge engineering 2007. Atlantis Press, DOI, (to appear in print).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Informatics and Information TechnologiesSlovak University of Technology in BratislavaBratislavaSlovak Republic

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