Abstract
Dynamic time warping (DTW) is one of the most important similarity measurement methods for time series analysis. In view of the high complexity and pathological alignment of DTW, a lot of variants of DTW have been proposed. However, the existing methods calculate the similarity between the original time series through dynamic programming directly, and ignore the characteristic that different components in the time series often have different degrees of importance. This paper proposes a time series similarity measurement method based on series decomposition and fast DTW, which combines time series decomposition method and DTW method. Series decomposition is an important means of time series analysis which can decompose time series into trend, seasonality, and remainder components. In this paper, after using the Seasonal-Trend decomposition using Loess (STL) method to decompose the time series, the similarity between the trend components and the similarity between seasonal components are respectively measured. The impact of the more important component is amplified, and then the comprehensive similarity measurement result will be obtained. Experimental results on 20 UCR time series datasets show that, compared with the existing fast DTW and constrained DTW and their variants, the method proposed in this paper achieves a higher classification accuracy. Simultaneously, combining the advantage of low complexity of fast DTW, the computational complexity of proposed method is still first-order linearly related to the length of time series.
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References
Cheng C-H, Yang J-H (2018) Fuzzy time-series model based on rough set rule induction for forecasting stock price. Neurocomputing 302:33–45. https://doi.org/10.1016/j.neucom.2018.04.014
Lavrenz SM, Vlahogianni EI, Gkritza K, Ke Y (2018) Time series modeling in traffic safety research. Accid Anal Prev 117:368–380. https://doi.org/10.1016/j.aap.2017.11.030
Aljawarneh S, Anguera A, Atwood JW, Lara JA, Lizcano D (2019) Particularities of data mining in medicine: lessons learned from patient medical time series data analysis. EURASIP J Wirel Comm Netw 2019(1):1–29. https://doi.org/10.1186/s13638-019-1582-2
Baloch S, Muhammad MS (2021) An intelligent data mining-based fault detection and classification strategy for Microgrid. IEEE Access 9:22470–22479. https://doi.org/10.1109/ACCESS.2021.3056534
Tang G, Pang B, He Y, Tian T (2019) Gearbox fault diagnosis based on hierarchical instantaneous energy density dispersion entropy and dynamic time warping. Entropy, vol 21. https://doi.org/10.3390/e21060593
Lampert T, Lafabregue B, Gançarski P, Dao T-B-H, Serrette N, Vrain C et al (2018) Constrained distance based clustering for time-series: a comparative and experimental study. Data Min Knowl Discov 32(6):1663–1707. https://doi.org/10.1007/s10618-018-0573-y
Wang Y, Chu YM, Thaljaoui A, Khan YA, Chammam W, Abbas SZ (2021) A multi-feature hybrid classification data mining technique for human-emotion. BioData Mining 14(1):1–20. https://doi.org/10.1186/s13040-021-00254-x
Campbell E, Scheme E, Phinyomark A (2020) Current trends and confounding factors in myoelectric control: Limb position and contraction intensity. Sensors (Switzerland), vol 20. https://doi.org/10.3390/s20061613
He J, Guo Z, Shao Z, Dan G, Zhao J (2020) An LSTM-Based prediction method for lower limb intention perception by integrative analysis of kinect visual signal. Journal of Healthcare Engineering. https://doi.org/10.1155/2020/8024789
Ding H, Trajcevski G, Scheuermann P, Wang X, Keogh E. (2008) Querying and mining of time series data: experimental comparison of representations and distance measures. Proceedings of the VLDB Endowment
Rakthanmanon T, Campana B, Mueen A, Zhu Q, Zakaria J, Keogh E et al (2012) Searching and mining trillions of time series subsequences under dynamic time warping. In: Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. https://doi.org/10.1145/2339530.2339576, pp 262–270
Keogh E, Ratanamahatana CA (2005) Exact indexing of dynamic time warping. Knowl Inf Syst 7(3):358–386. https://doi.org/10.1007/s10115-004-0154-9
Cleveland RB, Cleveland WS (1990) STL: A Seasonal-trend decomposition procedure based on Loess. J Off Stat 6(1): 3–73
Ding I-J, Shi J-Y (2017) Kinect microphone array-based speech and speaker recognition for the exhibition control of humanoid robots. Comput Electr Eng 62:719–729. https://doi.org/10.1016/j.compeleceng.2015.12.010
Zadghorban M, Nahvi M (2018) An algorithm on sign words extraction and recognition of continuous Persian sign language based on motion and shape features of hands. Pattern Anal Appl 21(2):323–335. https://doi.org/10.1007/s10044-016-0579-2
Sakoe H, Chiba S (1971) A dynamic programming approach to continuous speech recognition. In: Proceedings of the seventh international congress on acous-tics, pp 65–69
Sakoe H, Chiba S (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Trans Signal Process 26(1):43–49. https://doi.org/10.1109/TASSP.1978.1163055
Itakura F (1975) Minimum prediction residual principle applied to speech recognition. IEEE Trans Signal Process 23(1):67–72. https://doi.org/10.1109/TASSP.1975.1162641
Salvador S, Chan P (2007) FastDTW: Toward accurate dynamic time warping in linear time and space. Intell Data Anal 11(5):561–580. https://doi.org/10.3233/IDA-2007-11508
Choi W, Cho J, Lee S, Jung Y (2020) Fast constrained dynamic time warping for similarity measure of time series data. IEEE Access 8:222841–222858. https://doi.org/10.1109/ACCESS.2020.3043839
Zhu Y, Keogh E, Imamura M, Nikovski D (2019) Introducing time series chains: a new primitive for time series data mining. Knowl Inf Syst 60(2):1135–1161. https://doi.org/10.1007/s10115-018-1224-8
Li H (2021) Time works well: Dynamic time warping based on time weighting for time series data mining. Inf Sci 547:592–608. https://doi.org/10.1016/j.ins.2020.08.089
Zhang Z, Tavenard R, Bailly A, Tang X, Tang P, Corpetti T (2017) Dynamic Time Warping under limited warping path length. Inf Sci 393:91–107. https://doi.org/10.1016/j.ins.2017.02.018
Łuczak M (2016) Hierarchical clustering of time series data with parametric derivative dynamic time warping. Expert Syst Appl 62:116–130. https://doi.org/10.1016/j.eswa.2016.06.012
West M (1997) Time series decomposition. Biometrika 84(2):489–494. https://doi.org/10.1023/A:1021062510565
Ran AN, Xiaobo ZHU, Hanbing YAN (2017) Research on a Method of Data Theft Detection Based on Time Series Decomposition. Netinfo Security (8):76-82. https://doi.org/10.3969/j.issn.1671-1122.2017.08.011
Xing Y, Yue J, Chen C (2020) Interval estimation of landslide displacement prediction based on time series decomposition and long short-term memory network. IEEE Access 8:3187–3196. https://doi.org/10.1109/ACCESS.2019.2961295
Abdollahi H (2020) A novel hybrid model for forecasting crude oil price based on time series decomposition. Applied Energy. https://doi.org/10.1016/j.apenergy.2020.115035
Bell WR, Hillmer SC (2002) Issues involved with the seasonal adjustment of economic time series. J Bus Econ Stat 20(1):98–127
Findley DF, Monsell BC, Bell WR et al (1998) New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program. J Bus Econ Stat 16(2):127–152. https://doi.org/10.2307/1392565
Dokumentov A, Hyndman RJ (2015) STR: A Seasonal-Trend decomposition procedure based on regression. Monash Econometrics and Business Statistics Working Papers 13/15, Monash University, Department of Econometrics and Business Statistics
Wen Q, Gao J, Song X, Sun L, Xu H, Zhu S (2019) RobustSTL: A Robust Seasonal-trend decomposition algorithm for long time series. Proc Conf AAAI Artif Intell 33:5409–5416. https://doi.org/10.1609/aaai.v33i01.33015409
Dau HA, Keogh E, Kamgar K, Yeh CCM, Zhu Y, Gharghabi S, Ratanamahatana CA, Chen Y, Hu B, Begum N, Bagnall A, Mueen A, Batista G (2018) The UCR time series classification archive. https://www.cs.ucr.edu/eamonn/time_series_data_2018/
Petitjean F, Webb GI, Nicholson AE, Forestier G, Chen Y, 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):1–26. https://doi.org/10.1007/s10115-015-0878-8
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Xiaoxuan Han, Yang Jin, Gang Xiang and Yan Shi are contributed equally to this work.
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Zhang, Q., Zhang, C., Cui, L. et al. A method for measuring similarity of time series based on series decomposition and dynamic time warping. Appl Intell 53, 6448–6463 (2023). https://doi.org/10.1007/s10489-022-03716-9
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DOI: https://doi.org/10.1007/s10489-022-03716-9