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Exploring interval implicitization in real-valued time series classification and its applications

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Abstract

Due to the fact of uncertainty contained in observed real-valued time series, the aim of this paper is to explore interval implicitization in real-valued time series classification problems. A novel real-valued time series classification method under the transformed implicit interval-valued data environment is developed, namely 1NN-IDTW. To do this, by utilizing the ARIMA model, real-valued time series are first converted in parallel to interval-valued time series. Then, the integration of explored interval implicitization process, Dynamic Time Warping algorithm and the simple nearest neighbor classifier is proposed. In the numerical experimental part, the developed 1NN-IDTW is first directly applied to randomly selected 16 real-world datasets from the UCR time series archive for time series classification. The explored interval implicitization process is also integrated with different classification models, so as to verity its performance. The results indicate that our developed model performs better on 13 datasets over 6 baselines. Furthermore, comparing with existed time series classification methods, the integration of interval implicitization can improve the prediction accuracy by more than 10%.

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No data were used to support the findings of the study performed.

Notes

  1. For the sake of comparison, the parameters \(\omega _\alpha\) and \(\omega _\beta\) in the D’Urso-Giovanni distance are, respectively, set as \(\omega _\alpha =0.7, \omega _\beta =0.3\) according to Wang et al. [48].

  2. https://www.cs.ucr.edu/ eamonn/time_series_data_2018/.

References

  1. Juez C, Garijo N, Hassan MA, Nadal-Romero E (2021) Intraseasonal-to-interannual analysis of discharge and suspended sediment concentration time-series of the upper changjiang (yangtze river). Water Resour Res 57:e2020WR029457

    Google Scholar 

  2. Pirasteh S, Zenner EK, Mafi-Gholami D, Jaafari A, Li J (2021) Modeling mangrove responses to multi-decadal climate change and anthropogenic impacts using a long-term time series of satellite imagery. Int J Appl Earth Obs Geoinf 102:102390

    Google Scholar 

  3. Savadkoohi M, Oladunni T, Thompson LA (2021) Deep neural networks for human’s fall-risk prediction using force-plate time series signal. Expert Syst Appl 182:115220

    Google Scholar 

  4. Hou X, Wang K, Zhong C, Wei Z (2021) St-trader: a spatial-temporal deep neural network for modeling stock market movement. IEEE/CAA J Autom Sin 8(5):1015–1024

    Google Scholar 

  5. Takyi PO, Bentum-Ennin I (2020) The impact of covid-19 on stock market performance in Africa: a bayesian structural time series approach. J Econ Bus 115(7):105968

    Google Scholar 

  6. Devi M, Kumar J, Malik DP, Mishra P (2021) Forecasting of wheat production in haryana using hybrid time series model. J Agric FoodRes 12:100175

    Google Scholar 

  7. Liu XL, Lin Z, Feng ZM (2021) Short-term offshore wind speed forecast by seasonal ARIMA - a comparison against GRU and LSTM. Energy 227:120492

    Google Scholar 

  8. Zeng Z, Li M, Hyndman RJ (2021) Bayesian median autoregression for robust time series forecasting. Int J Forecast 37(2):1000–1010

    Google Scholar 

  9. Scotch CG, Murgulet D, Constantz J (2021) Time-series temperature analyses indicate conduction and diffusion are dominant heat-transfer processes in fine sediment, low-flow streams. Sci Total Environ 768(8):144367

    Google Scholar 

  10. Yang Q, Liu D, Fang Y, Yang D, Zhou Y, Sheng Z (2020) Research on a hybrid EMD-SVR model for time series prediction. Springer, Cham

    Google Scholar 

  11. Liu Z, Liu J (2020) A robust time series prediction method based on empirical mode decomposition and high-order fuzzy cognitive maps. Knowl Based Syst 203(5):106105

    Google Scholar 

  12. Karevan Z, Suykens J (2020) Transductive LSTM for time-series prediction: an application to weather forecasting. Neural Netw 125:1–9

    Google Scholar 

  13. Fan C, Matkovic K, Hauser H (2021) Sketch-based fast and accurate querying of time series using parameter-sharing LSTM networks. IEEE Trans Visual Comput Graph 27(12):4495–4506

    Google Scholar 

  14. Shen ZP, Zhang YM, Lu JW, Xu J, Xiao G (2020) A novel time series forecasting model with deep learning. Neurocomputing 396:302–313

    Google Scholar 

  15. Guo J, Lu W, Yang JH, Liu XD (2021) A rule-based granular model development for interval-valued time series. Int J Approx Reason 136:201–222

    MathSciNet  MATH  Google Scholar 

  16. Yang DC, Guo JE, Sun SL, Han J, Wang SY (2022) An interval decomposition-ensemble approach with data-characteristic-driven reconstruction for short-term load forecasting. Appl Energy 306(Part A):117992

    Google Scholar 

  17. Zhou W, Chen Y, Ding S, Chen L, Li R (2020) A grey seasonal least square support vector regression model for time series forecasting. ISA Trans 114(11):82–98

    Google Scholar 

  18. Yao H, Zhang QX, Niu GY, Liu H, Yang YX (2021) Applying the GM(1,1) model to simulate and predict the ecological footprint values of suzhou city, china. Environ Dev Sustain 23:11297–11309

    Google Scholar 

  19. Huang HL, Tao ZF, Liu JP, Cheng JH, Chen HY (2021) Exploiting fractional accumulation and background value optimization in multivariate interval grey prediction model and its application. Eng Appl Artif Intell 104:104360

    Google Scholar 

  20. Kahraman MU, Aydemir E (2020) A bibjective inventory routing problem with interval grey demand data. Grey Syst Theory Appl 10(2):193–214

    Google Scholar 

  21. Chen HC, Wei DQ (2021) Chaotic time series prediction using echo state network based on selective opposition grey wolf optimizer. Nonlinear Dyn 104:3925–3935

    Google Scholar 

  22. Bhaskar N, Philip NY, Manikandan S (2021) Time series classification based correlational neural network with bidirectional LSTM for automated detection of kidney disease. IEEE Sens J 21(4):4811–4818

    Google Scholar 

  23. Medico R, Ruyssinck J, Deschrijver D, Dhaene T (2021) Learning multivariate shapelets with multi-layer neural networks for interpretable time-series classification. Adv Data Anal Classif 15:911–936

    MathSciNet  MATH  Google Scholar 

  24. Hlab C, Jla B, Zy C, Rwla B, Kw D, Yuan WE (2020) Adaptively constrained dynamic time warping for time series classification and clustering. Inf Sci 534:97–116

    MathSciNet  Google Scholar 

  25. Cabrera D, Sancho F, Cerrada M, Snchez R, Li C (2020) Knowledge extraction from deep convolutional neural networks applied to cyclo-stationary time-series classification. Inf Sci 524:1–14

    MathSciNet  MATH  Google Scholar 

  26. Abdu-Aguye MB, Gomaa W, Makihara Y, Yagi Y (2022) Investigating strategies towards adversarially robust time series classification. Pattern Recogn Lett 156:104–111

    Google Scholar 

  27. Li HL, Jia RY, Wan XJ (2022) Time series classification based on complex network. Expert Syst Appl 194:116502

    Google Scholar 

  28. Liu P, Sun X, Han Y, He Z, Zhang W, Wu C (2022) Arrhythmia classification of lstm autoencoder based on time series anomaly detection. Biomed Signal Process Control 71:103228

    Google Scholar 

  29. Reiter W (2021) Co-occurrence balanced time series classification for the semi-supervised recognition of surgical smoke. Int J Comput Assist Radiol Surg 16(1):2021–2027

    Google Scholar 

  30. Thaker J, Hller R (2022) A comparative study of time series forecasting of solar energy based on irradiance classification. Energies 15(8):1–26

    Google Scholar 

  31. Petitjean F, Forestier G, Webb GI, Nicholson AE, Chen YP, Keogh E (2016) Faster and more accurate classification of time series by exploiting a novel dynamic time warping averaging algorithm. Knowl Inf Syst 47:1–26

    Google Scholar 

  32. Zhu B, Jiang Y, Gu M, Deng Y (2021) A GPU acceleration framework for motif and discord based pattern mining. IEEE Trans Parallel Distrib Syst 32(8):1987–2004

    Google Scholar 

  33. Alaee S, Mercer R, Kamgar K, Keogh E (2021) Time series motifs discovery under dtw allows more robust discovery of conserved structure. Data Min Knowl Disc 35:863–910

    MathSciNet  MATH  Google Scholar 

  34. Abanda A, Mori U, Lozano JA (2019) A review on distance based time series classification. Data Min Knowl Disc 33:378–412

    MathSciNet  MATH  Google Scholar 

  35. Han T, Peng QK, Zhu ZB, Shen YQ, Abid NN (2020) A pattern representation of stock time series based on dtw. Physica A 550:124–161

    MATH  Google Scholar 

  36. Li N, Jiang J, Wang W (2010) Interval implicitization of parametric surfaces. In: Zhu R, Zhang Y, Liu B, Liu C (eds) Information Computing and Applications. ICICA 2010. Lecture Notes in Computer Science, vol 6377. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16167-4_61

  37. Moore RE (1979) Methods and applications of interval analysis. SIAM studies in applied mathematics, society for industrial and applied mathematics SIAM, Philadelphia Pa

    MATH  Google Scholar 

  38. Ichino M, Yaguchi H (1994) Generalized minkowski metrics for mixed featuretype data analysis. IEEE Trans Syst Man Cybern 24(4):698–708

    MATH  Google Scholar 

  39. de Souza RM, de Carvalho FdA. (2004) Clustering of interval data based on cityblock distances. Pattern Recogn Lett 25(3):353–365

    Google Scholar 

  40. de Souza LC, de Souza RM, do Amaral GJA. (2020) Dynamic clustering of interval data based on hybrid lq distance. Knowl Inf Syst 62:687–718

    Google Scholar 

  41. Chen Y, Billard L (2019) A study of divisive clustering with hausdorff distances for interval data. Pattern Recogn 96:106969

    Google Scholar 

  42. DUrso P, Giordani P. (2006) A weighted fuzzy c-means clustering model for fuzzy data. Comput Stat Data Anal 50(6):1496–1523

    MathSciNet  MATH  Google Scholar 

  43. Irpino A, Verde R (2008) Dynamic clustering of interval data using a wasserstein-based distance. Pattern Recogn Lett 29(11):1648–1658

    MATH  Google Scholar 

  44. Keogh E, Ratanamahatana CA (2005) Exact indexing of dynamic time warping. Knowl Inf Syst 7(3):358–386

    Google Scholar 

  45. Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley

  46. Saito N (1994) Local feature extraction and its applications using a library of bases. Yale University

  47. Hoang AD, Anthony B, Kaveh K et al (2019) The ucr time series archive. IEEE/CAA J Autom Sin 6(06):6–18

    Google Scholar 

  48. Wang X, Yu F, Pedrycz W, Yu L (2019) Clustering of interval-valued time series of unequal length based on improved dynamic time warping. Expert Syst Appl 125:293–304

    Google Scholar 

  49. Wei W, Gu H, Deng W et al (2022) ABL-TC: a lightweight design for network traffic classification empowered by deep learning. Neurocomputing 489:333–344

    Google Scholar 

  50. Islam TU, Hasan MK, Lee YK, Lee S (2008) Enhanced 1-NN time series classification using badness of records. International Conference on Ubiquitous Information Management & Communication. ACM, 108-113

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Acknowledgements

The authors first want to thank the Editors and anonymous reviewers for their constructive and valuable comments, which have greatly improved the paper. The authors also want to thank Dr. Shahid Hussain Gurmani for proofreading the revised manuscript.

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Authors and Affiliations

  1. School of Big Data and Statistics, Anhui University, Hefei, 230601, Anhui, China

    Zhifu Tao & Bingxin Yao

  2. Center for Financial and Statistical Research, Anhui University, Hefei, 230061, Anhui, China

    Zhifu Tao

  3. School of Internet, Anhui University, Hefei, 230601, Anhui, China

    Jiaming Zhu

  4. Research Center for Applied Mathematics Research, Anhui University, Hefei, 230601, Anhui, China

    Jiaming Zhu

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Correspondence to Jiaming Zhu.

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The work was supported by the Humanities and Social Sciences Research Youth Project of the Ministry of Education of China (No. 21YJCZH148), the Natural Science Foundation of Anhui Province (Nos. 2108085MG239, 2008085QG334), the Humanities and Social Science Research Project of Universities in Anhui Province (No. SK2020A0049), the National Natural Science Foundation of China (Nos. 71871001, 72071001 and 72001001) and the Provincial Natural Science Research Project of Anhui Colleges (No. KJ2020A0004).

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Tao, Z., Yao, B. & Zhu, J. Exploring interval implicitization in real-valued time series classification and its applications. J Supercomput 79, 3373–3391 (2023). https://doi.org/10.1007/s11227-022-04792-x

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