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Improving temporal predictions through time-series labeling using matrix profile and motifs

  • S.I.: Deep Learning for Time Series Data
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Abstract

One of the most challenging tasks in time-series prediction is a model’s capability to accurately learn the repeating granular trends in the data’s structure to generate effective predictions. Traditionally specially tuned statistical models and deep learning models like recurrent neural networks and long short-term memory networks are used to tackle such problem of sequence modeling. However in practice, factors like inadequate parameters in case of statistical models, random weight initializations, and data inadequacy in case of deep learning models affect the resulting final predictions. As a possible solution to these known problems, this paper introduces a novel method of time-series labeling (TSL) comprising a combination of encoding and decoding methodologies that not only takes into account the granular structure of a time-series data but also its underlying meta-learners for better predictive accuracy. To demonstrate the approach’s effectiveness and capability of handling wide range of scenarios, comparisons are drawn first over different widely used statistical and deep learning models and then applying TSL to each of them in order to showcase the resulting performance improvement when implemented over a wide variety of real-world datasets. The experimental findings reflect an average of 25% increase in overall performance when using TSL along with mostly similar performance of different combinations regardless of model complexity thereby proving its efficacy in predicting periodic data.

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References

  1. Das R, Middya AI, Roy S (2021) High granular and short term time series forecasting of pm2.5 air pollutant - a comparative review. Artif Intell Rev. https://doi.org/10.1007/s10462-021-09991-1

  2. Middya AI, Roy S, Das R (2021) Spatiotemporal variability analysis of air pollution data from iot based participatory sensing. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-021-03536-8

    Article  Google Scholar 

  3. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput. https://doi.org/10.1162/neco.1997.9.8.1735

    Article  Google Scholar 

  4. Box GEP, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: Forecasting and control, 5th edn. Wiley

  5. Chang X, Gao M, Wang Y, Hou X (2012) Seasonal autoregressive integrated moving average model for precipitation time series. J Math Stat 8:500–505. https://doi.org/10.3844/jmssp.2012.500.505

    Article  Google Scholar 

  6. Al-Hmouz R, Pedrycz W, Balamash A (2015) Description and prediction of time series: a general framework of granular computing. Expert Syst Appl 42:1. https://doi.org/10.1016/j.eswa.2015.01.060

    Article  Google Scholar 

  7. Chiu B, Keogh E, Lonardi S (2003) Probabilistic discovery of time series motifs. KDD ’03. Association for Computing Machinery, New York, NY, USA. https://doi.org/10.1145/956750.956808

  8. Caruana R, Lawrence S, Giles L (2000) Overfitting in neural nets: backpropagation, conjugate gradient, and early stopping. In: Proceedings of the 13th international conference on neural information processing systems, NIPS’00. MIT Press, pp 381–387

  9. Leite D, Škrjanc I (2019) Ensemble of evolving optimal granular experts, owa aggregation, and time series prediction. Inform Sci 504:95–112. https://doi.org/10.1016/j.ins.2019.07.053

    Article  MathSciNet  Google Scholar 

  10. Shao K, Zheng J, Wang H, Xu F, Wang X, Liang B (2021) Recursive sliding mode control with adaptive disturbance observer for a linear motor positioner. Mech Syst Signal Process 146:107,014. https://doi.org/10.1016/j.ymssp.2020.107014

  11. Shao K, Zheng J, Wang H, Wang X, Lu R, Man Z (2021) Tracking control of a linear motor positioner based on barrier function adaptive sliding mode. IEEE Trans Ind Inf 17(11):7479–7488. https://doi.org/10.1109/TII.2021.3057832

    Article  Google Scholar 

  12. Shao K (2021) Nested adaptive integral terminal sliding mode control for high-order uncertain nonlinear systems. Int J Robust Nonlinear Control 31(14):6668–6680. https://doi.org/10.1002/rnc.5631

    Article  MathSciNet  Google Scholar 

  13. Afolabi D, Guan SU, Man KL, Wong PWH, Zhao X (2017) Hierarchical meta-learning in time series forecasting for improved interference-less machine learning 9(11):1. https://doi.org/10.3390/sym9110283

  14. Nath P, Saha P, Middya AI, Roy S (2021) Long-term time-series pollution forecast using statistical and deep learning methods. Neural Comput Appl 33(19):12551–12570. https://doi.org/10.1007/s00521-021-05901-2

    Article  Google Scholar 

  15. Middya AI, Roy S, Dutta J, Das R (2020) JUSense: a unified framework for participatory-based urban sensing system. Mob Networks Appl 25(4):1249–1274. https://doi.org/10.1007/s11036-020-01539-x

    Article  Google Scholar 

  16. Dutta J, Chowdhury C, Roy S, Middya AI, Gazi F (2017) Towards smart city: sensing air quality in city based on opportunistic crowd-sensing. In: Proceedings of the 18th international conference on distributed computing and networking, pp. 1–6. https://doi.org/10.1145/3007748.3018286

  17. Middya AI, Roy S (2021) Spatial interpolation techniques on participatory sensing data. ACM Trans Spat Alg Syst 7(3):1–32

    Google Scholar 

  18. Kar D, Middya AI, Roy S (2019) An approach to detect travel patterns using smartphone sensing. In: IEEE international conference on advanced networks and telecommunications systems (ANTS). IEEE. https://doi.org/10.1109/ants47819.2019.9118073

  19. Patra S, Middya AI, Roy S (2021) PotSpot: Participatory sensing based monitoring system for pothole detection using deep learning. Multimed Tools Appl 80(16):25171–25195. https://doi.org/10.1007/s11042-021-10874-4

    Article  Google Scholar 

  20. Middya AI, Ray B, Roy S (2020) Auction based resource allocation mechanism in federated cloud environment: TARA. IEEE Trans Services Comput 1:1. https://doi.org/10.1109/tsc.2019.2952772

    Article  Google Scholar 

  21. Bose B, Dutta J, Ghosh S, Pramanick P, Roy S (2018) D&RSense: detection of driving patterns and road anomalies. In: 3rd International conference on internet of things: smart innovation and usages (IoT-SIU). IEEE. https://doi.org/10.1109/iot-siu.2018.8519861

  22. Rehena Z, Mukherjee R, Roy S, Mukherjee N (2014) Detection of node failure in wireless sensor networks. In: Applications and innovations in mobile computing (AIMoC). IEEE. https://doi.org/10.1109/aimoc.2014.6785531

  23. Ghosh K, Roy S, Das PK (2009) An alternative approach to find the fermat point of a polygonal geographic region for energy efficient geocast routing protocols: global minima scheme. In: 1st International conference on networks & communications. IEEE https://doi.org/10.1109/netcom.2009.30

  24. Middya AI, Roy S (2021) Geographically varying relationships of COVID-19 mortality with different factors in India. Sci Rep 11(1):1. https://doi.org/10.1038/s41598-021-86987-5

    Article  Google Scholar 

  25. Dong R, Pedrycz W (2008) A granular time series approach to long-term forecasting and trend forecasting. Physica A Stat Mech Appl 387(13):3253–3270. https://doi.org/10.1016/j.physa.2008.01.095

    Article  Google Scholar 

  26. Froelich W, Pedrycz W (2017) Fuzzy cognitive maps in the modeling of granular time series. Knowl-Based Syst 115:110–122. https://doi.org/10.1016/j.knosys.2016.10.017

    Article  Google Scholar 

  27. Deng W, Wang G, Zhang X, Xu J, Li G (2016) A multi-granularity combined prediction model based on fuzzy trend forecasting and particle swarm techniques. Neurocomputing 173:1671–1682. https://doi.org/10.1016/j.neucom.2015.09.040

    Article  Google Scholar 

  28. Jana RK, Ghosh I, Sanyal MK (2020) A granular deep learning approach for predicting energy consumption. Applied Soft Computing 89, 106,091. https://doi.org/10.1016/j.asoc.2020.106091

  29. Rule induction for forecasting method selection (2009) Meta-learning the characteristics of univariate time series. Neurocomputing 72(10):2581–2594. https://doi.org/10.1016/j.neucom.2008.10.017

    Article  Google Scholar 

  30. Gordon J, Bronskill J, Bauer M, Nowozin S, Turner RE (2019) Meta-learning probabilistic inference for prediction. In: 7th International conference on learning representations, ICLR 2019, New Orleans, LA, USA, May 6–9, 2019. OpenReview.net. https://openreview.net/forum?id=HkxStoC5F7

  31. Yao H, Liu Y, Wei Y, Tang X, Li Z (2019) Learning from multiple cities: A meta-learning approach for spatial-temporal prediction. Association for Computing Machinery, New York, NY, USA. https://doi.org/10.1145/3308558.3313577

  32. Zhou S, Lai KK, Yen J (2012) A dynamic meta-learning rate-based model for gold market forecasting. Expert Syst Appl 39(6):6168–6173. https://doi.org/10.1016/j.eswa.2011.11.115

    Article  Google Scholar 

  33. Guo H, Pedrycz W, Liu X (2018) Hidden markov models based approaches to long-term prediction for granular time series. IEEE Trans Fuzzy Syst 26(5):2807–2817. https://doi.org/10.1109/TFUZZ.2018.2802924

    Article  Google Scholar 

  34. Leite D, Gomide F, Ballini R, Costa P (2011) Fuzzy granular evolving modeling for time series prediction. In: IEEE international conference on fuzzy systems (FUZZ-IEEE 2011), pp 2794–2801 https://doi.org/10.1109/FUZZY.2011.6007452

  35. Lemke C, Gabrys B (2010) Meta-learning for time series forecasting and forecast combination. Neurocomputing 73(10):2006–2016. https://doi.org/10.1016/j.neucom.2009.09.020

    Article  Google Scholar 

  36. Ali AR, Gabrys B, Budka M (2018) Cross-domain meta-learning for time-series forecasting. Procedia Comput Sci 126:9–18. https://doi.org/10.1016/j.procs.2018.07.204

    Article  Google Scholar 

  37. Abraham A (2004) Meta learning evolutionary artificial neural networks. Neurocomputing 56:1–38. https://doi.org/10.1016/S0925-2312(03)00369-2

    Article  Google Scholar 

  38. Cecaj A, Lippi M, Mamei M, Zambonelli F (2020) Comparing deep learning and statistical methods in forecasting crowd distribution from aggregated mobile phone data. Appl Sci 10:1. https://doi.org/10.3390/app10186580

    Article  Google Scholar 

  39. Yeh CM, Zhu Y, Ulanova L, Begum N, Ding Y, Dau HA, Silva DF, Mueen A, Keogh E (2016) Matrix profile i: All pairs similarity joins for time series: a unifying view that includes motifs, discords and shapelets. In: IEEE 16th International Conference on Data Mining (ICDM), pp 1317–1322. https://doi.org/10.1109/ICDM.2016.0179

  40. Law SM (2019) Stumpy: a powerful and scalable python library for time series data mining. J Open Source Softw 4(39):1504. https://doi.org/10.21105/joss.01504

    Article  Google Scholar 

  41. Zhu Y, Imamura M, Nikovski D, Keogh E (2017) Matrix profile vii: Time series chains: A new primitive for time series data mining (best student paper award). In: IEEE international conference on data mining (ICDM). https://doi.org/10.1109/ICDM.2017.79

  42. Ministry of Environment, Forest and Climate Change, Govt. of India: Central Pollution Control Board. http://www.cpcb.nic.in/. Accessed: 31 March 2021

  43. Sudalai Raj Kumar: Daily Temperature of Major Cities (2020). https://www.kaggle.com/sudalairajkumar/daily-temperature-of-major-cities

  44. Zielak: Bitcoin Historical Data (2021). https://www.kaggle.com/mczielinski/bitcoin-historical-data

  45. Bisong E (2019). Google Colaboratory. https://doi.org/10.1007/978-1-4842-4470-8_7

  46. Google colaboratory. https://colab.research.google.com. Accessed 31 March 2021

  47. Van Rossum G, Drake FL Jr (1995) Python tutorial. Centrum voor Wiskunde en Informatica Amsterdam

  48. van der Walt S, Colbert SC, Varoquaux G (2011) The numpy array: a structure for efficient numerical computation. Comput Sci Eng 13(2):22–30

    Article  Google Scholar 

  49. Martín Abadi et al. (2015) Tensorflow:large-scale machine learning on heterogeneous systems

  50. Seasonal decomposition by moving averages. https://www.statsmodels.org/stable/_modules/statsmodels/tsa/seasonal.html#seasonal_decompose. Accessed 03 March 2021

  51. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E (2011) Scikit-learn: machine learning in Python. J Mach Learn Res 12:2825–2830

    MathSciNet  MATH  Google Scholar 

  52. US Department of State: air now international US embassies and consulates. https://www.airnow.gov/international/us-embassies-and-consulates/. Accessed 31 March 2021

  53. Kaggle. https://www.kaggle.com/. Accessed 31 March 2021

  54. Kissock JK (2021) Unversity of Dayton average daily temperature archive. http://academic.udayton.edu/kissock/http/Weather/. Accessed 03 March 2021

  55. Seabold S, Perktold J (2010) Statsmodels: Econometric and statistical modeling with python. In: Proceedings of the 9th python in science conference, p 1. https://conference.scipy.org/proceedings/scipy2010/pdfs/seabold.pdf

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Acknowledgements

The research work of Asif Iqbal Middya is funded by “NET-JRF (National Eligibility Test-Junior Research Fellowship) scheme of the University Grants Commission, Government of India”. This research work is also supported by the project entitled “Participatory and Realtime Pollution Monitoring System For Smart City, funded by Higher Education, Science & Technology and Biotechnology, Department of Science & Technology, Government of West Bengal, India”.

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Correspondence to Sarbani Roy.

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Saha, P., Nath, P., Middya, A.I. et al. Improving temporal predictions through time-series labeling using matrix profile and motifs. Neural Comput & Applic 34, 13169–13185 (2022). https://doi.org/10.1007/s00521-021-06744-7

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