Robust shapelet representation method for time series

doi:10.11772/j.issn.1001-9081.2024020163

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (2): 436-443.DOI: 10.11772/j.issn.1001-9081.2024020163

• Data science and technology • Previous Articles

Robust shapelet representation method for time series

Qianting ZHANG¹^,², Liying HU¹^,², Lifei CHEN¹^,²^,³()

^1.College of Computer and Cyber Security，Fujian Normal University，Fuzhou Fujian 350117，China
^2.Digital Fujian Internet?of?Things Laboratory of Environmental Monitoring （Fujian Normal University），Fuzhou Fujian 350117，China
^3.Center for Applied Mathematics of Fujian Province （Fujian Normal University），Fuzhou Fujian 350117，China

Received:2024-02-19 Revised:2024-03-24 Accepted:2024-04-01 Online:2024-06-04 Published:2025-02-10
Contact: Lifei CHEN
About author:ZHANG Qianting， born in 1995， M. S. candidate. Her research interests include data mining， machine learning.
HU Liying， born in 1979， Ph. D.， associate professor. Her research interests include data mining， machine learning， target detection.
Supported by:
National Natural Science Foundation of China(U1805263)

时间序列的鲁棒形态表征方法

张倩婷¹^,², 胡丽莹¹^,², 陈黎飞¹^,²^,³()

^1.福建师范大学计算机与网络空间安全学院，福州 350117
^2.数字福建环境监测物联网实验室（福建师范大学），福州 350117
^3.福建省应用数学中心（福建师范大学），福州 350117

通讯作者: 陈黎飞
作者简介:张倩婷（1995—），女，福建惠安人，硕士研究生，主要研究方向：数据挖掘、机器学习
胡丽莹（1979—），女，浙江缙云人，副教授，博士，主要研究方向：数据挖掘、机器学习、目标检测；
基金资助:
国家自然科学基金资助项目(U1805263)

Abstract

Abstract:

In view of the wide application of time series data in various fields， the mining and representation of identifiable features of the data is crucial. Due to the influence of the data acquisition environment and acquisition equipment， time series data in many application fields are characterized by high noise， which puts forward high requirements for the robustness of data representation methods. Therefore， a Robust Shapelet representation method for Time series （TRS） was proposed， which adopts the feature extraction method of Key-Shapelet （KS）， retains the interpretability while reducing the influence of noise， and represents the time series by position distance measurement， thereby improving the robustness of the whole method. Experimental results on noise-disturbed time series data show that the features extracted by TRS are significantly better than those of the existing methods in classification， and the average accuracy of TRS is 2.1 percentage points higher than that of the deep learning model — Adversarial Dynamic Shapelet Network （ADSN）， which also extracts features based on Shapelets. It can be seen that the feature set extracted by TRS is more representative and robust.

Key words: time series, Key-Shapelet (KS), noise, robustness, representation

摘要：

鉴于时间序列数据在各个领域的广泛应用，对这些数据的可辨识特征的挖掘和表征至关重要。受数据采集环境和采集设备的影响，许多应用领域的时序数据都存在高噪声的特点，这对数据表征方法的鲁棒性提出了很高的要求。因此，提出一种时间序列的鲁棒形态表征方法（TRS）。该方法采用关键形态（KS）的特征提取方法，在保留可解释性的同时减少噪声的影响，并通过位置距离度量对时间序列进行表征，从而提高整个方法的鲁棒性。在受噪声干扰的时间序列数据上的实验结果表明，TRS所提取的特征在分类上显著均优于现有的方法，与同样基于形态模式提取特征的深度学习模型——对抗动态Shapelet网络（ADSN）相比，平均正确率高出2.1个百分点。可见，TRS提取的特征集更有代表性和鲁棒性。

关键词: 时间序列, 关键形态, 噪声, 鲁棒性, 表征

CLC Number:

TP301.6

Qianting ZHANG, Liying HU, Lifei CHEN. Robust shapelet representation method for time series[J]. Journal of Computer Applications, 2025, 45(2): 436-443.

张倩婷, 胡丽莹, 陈黎飞. 时间序列的鲁棒形态表征方法[J]. 《计算机应用》唯一官方网站, 2025, 45(2): 436-443.

Figures/Tables 13

References 23

1	魏池璇，王志海，原继东，等. 时间序列可变尺度的时频特征求解及其分类［J］. 软件学报， 2022， 33（12）： 4411-4428.
	WEI C X， WANG Z H， YUAN J D， et al. Time series pattern discovery and classification with variable scales in time-frequency domains［J］. Journal of Software， 2022， 33（12）： 4411-4428.
2	WANG J， CHEN Y， HAO S， et al. Deep learning for sensor-based activity recognition： a survey［J］. Pattern Recognition Letters， 2019， 119： 3-11.
3	RAJKOMAR A， OREN E， CHEN K， et al. Scalable and accurate deep learning with electronic health records［J］. npj Digital Medicine， 2018， 1： No.18.
4	任守纲，张景旭，顾兴健，等. 时间序列特征提取方法研究综述［J］. 小型微型计算机系统， 2021， 42（2）： 271-278.
	REN S G， ZHANG J X， GU X J， et al. Overview of feature extraction algorithms for time series［J］. Journal of Chinese Computer Systems， 2021， 42（2）： 271-278.
5	罗伟. 基于时间序列表征的检索与分类研究［D］. 济南：山东大学， 2022.
	LUO W. Research on time series representation based retrieval and classification［D］. Jinan： Shandong University， 2022.
6	DILMI M D， BARTHÈS L， MALLET C， et al. Iterative Multiscale Dynamic Time Warping （IMs-DTW）： a tool for rainfall time series comparison［J］. International Journal of Data Science Analytics， 2020， 10（1）： 65-79.
7	PETITJEAN F， FORESTIER G， WEBB G I， et al. Dynamic time warping averaging of time series allows faster and more accurate classification［C］// Proceedings of the 2014 IEEE International Conference on Data Mining. Piscataway： IEEE， 2014： 470-479.
8	ISMAIL FAWAZ H， LUCAS B， FORESTIER G， et al. InceptionTime： finding AlexNet for time series classification［J］. Data Mining and Knowledge Discovery， 2020， 34（6）： 1936-1962.
9	DEMPSTER A， PETITJEAN F， WEBB G I. ROCKET： exceptionally fast and accurate time series classification using random convolutional kernels［J］. Data Mining and Knowledge Discovery， 2020， 34： 1454-1495.
10	DEMPSTER A， SCHMIDT D F， WEBB G I. MiniRocket： a very fast （almost） deterministic transform for time series classification［C］// Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. New York： ACM， 2021： 248-257.
11	YE L， KEOGH E. Time series shapelets： a new primitive for data mining［C］// Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York： ACM， 2009： 947-956.
12	LINES J， DAVIS L M， HILLS J， et al. A shapelet transform for time series classification［C］// Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York： ACM， 2012： 289-297.
13	RAKTHANMANON T， KEOGH E. Fast shapelets： a scalable algorithm for discovering time series shapelets［C］// Proceedings of the 2013 SIAM International Conference on Data Mining. Philadelphia， PA： SIAM， 2013： 668-676.
14	GRABOCKA J， SCHILLING N， WISTUBA M， et al. Learning time-series shapelets［C］// Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York： ACM， 2014： 392-401.
15	ZHANG Z， ZHANG H， WEN Y， et al. Accelerating time series shapelets discovery with key points［C］// Proceedings of the 2016 Asia-Pacific Web Conference， LNCS 9932. Cham： Springer， 2016： 330-342.
16	JI C， ZHAO C， PAN L， et al. A fast shapelet discovery algorithm based on important data points［J］. International Journal of Web Services Research， 2017， 14（2）： 67-80.
17	BOSTROM A， BAGNALL A. Binary shapelet transform for multiclass time series classification［C］// Proceedings of the 2015 Big Data Analytics and Knowledge Discovery， LNCS 9263. Cham： Springer， 2015： 257-269.
18	LI G， CHOI B， XU J， et al. Efficient shapelet discovery for time series classification［J］. IEEE Transactions on Knowledge and Data Engineering， 2022， 34（3）： 1149-1163.
19	MA Q， ZHUANG W， COTTRELL G. Triple-shapelet networks for time series classification［C］// Proceedings of the 2019 IEEE International Conference on Data Mining. Piscataway： IEEE， 2019： 1246-1251.
20	MA Q， ZHUANG W， LI S， et al. Adversarial dynamic shapelet networks［C］// Proceedings of the 34th AAAI Conference on Artificial Intelligence. Palo Alto： AAAI Press， 2020： 5069-5076.
21	YEH C C M， ZHU Y， ULANOVA L， et al. Matrix profile I： all pairs similarity joins for time series： a unifying view that includes motifs， discords and shapelets［C］// Proceedings of the IEEE 16th International Conference on Data Mining. Piscataway： IEEE， 2016： 1317-1322.
22	冯冠玺，马超，石小川，等. Kernel-Shapelets：基于卷积网络的特征子序列学习方法［J］. 软件导刊， 2023， 22（4）： 8-14.
	FENG G X， MA C， SHI X C， et al. Kernel-Shapelets： approach to learning Shapelets based on CNN［J］. Software Guide， 2023， 22（4）： 8-14.
23	DEMŠAR J. Statistical comparisons of classifiers over multiple datasets［J］. Journal of Machine Learning Research， 2006， 7： 1-30.

方法	时间复杂度	方法	时间复杂度
DWT	O（n²m³）	FS	O（nm²）
ST	O（n²m⁴）	BSPCOVER	O（In²m）
LTS	O（Inm²）	TRS	O（nm²）

方法	时间复杂度	方法	时间复杂度
DWT	O（n²m³）	FS	O（nm²）
ST	O（n²m⁴）	BSPCOVER	O（In²m）
LTS	O（Inm²）	TRS	O（nm²）

场景数据	样本数		类别数	长度
场景数据	训练集	测试集	类别数	长度
ECG200	100	100	2	96
ECG5000	500	4 500	5	140
ECGFiveDays	23	861	2	136
NonInvasiveFatalECGThorax1	1 800	1 965	42	750
NonInvasiveFatalECGThorax2	1 800	1 965	42	750
TwoLeadECG	613	370	2	235
CinECGTorso	40	1 380	4	1 639
Lightning7	70	73	7	319
MoteStrain	20	1 252	2	84
Phoneme	214	1 896	39	1 024
Plane	105	105	7	144
SonyAIBORobotSurface1	20	601	2	70
SonyAIBORobotSurface2	27	953	2	65
Wafer	100	100	4	275

场景数据	样本数		类别数	长度
场景数据	训练集	测试集	类别数	长度
ECG200	100	100	2	96
ECG5000	500	4 500	5	140
ECGFiveDays	23	861	2	136
NonInvasiveFatalECGThorax1	1 800	1 965	42	750
NonInvasiveFatalECGThorax2	1 800	1 965	42	750
TwoLeadECG	613	370	2	235
CinECGTorso	40	1 380	4	1 639
Lightning7	70	73	7	319
MoteStrain	20	1 252	2	84
Phoneme	214	1 896	39	1 024
Plane	105	105	7	144
SonyAIBORobotSurface1	20	601	2	70
SonyAIBORobotSurface2	27	953	2	65
Wafer	100	100	4	275

场景数据	LS	TSN	ADSN	BSPCOVER	InceptionTime	MiniRocket	TRS
ECG200	0.880	0.900	0.920	0.920	0.910	0.910	0.950
ECG5000	0.932	0.948	0.947	0.944	0.942	0.945	0.951
ECGFiveDays	1.000	1.000	1.000	1.000	1.000	1.000	1.000
NonInvasiveFatalECGThorax1	0.259	0.877	0.902	0.915	0.958	0.955	0.947
NonInvasiveFatalECGThorax2	0.770	0.902	0.917	0.938	0.959	0.969	0.969
TwoLeadECG	0.996	0.972	0.986	0.997	0.996	0.998	0.997
CinECGTorso	0.870	0.975	0.976	0.965	0.853	0.870	0.901
Lightning7	0.726	0.644	0.767	0.808	0.795	0.795	0.795
MoteStrain	0.883	0.908	0.906	0.911	0.894	0.931	0.942
Phoneme	0.218	0.216	0.227	0.207	0.337	0.292	0.361
Plane	1.000	1.000	1.000	1.000	0.942	1.000	1.000
SonyAIBORobotSurface1	0.810	0.857	0.915	0.883	0.879	0.890	0.948
SonyAIBORobotSurface2	0.875	0.909	0.940	0.935	0.952	0.918	0.942
Wafer	0.996	0.999	0.999	0.998	0.999	0.999	1.000
Average Accuracy	0.801	0.865	0.886	0.887	0.887	0.891	0.907
Average Rank	5.571	4.429	3.214	3.357	3.643	2.571	1.571
Wilcoxon Test p value	0.002	0.019	0.028	0.075	0.025	0.025	—

Robust shapelet representation method for time series

时间序列的鲁棒形态表征方法

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 13

References 23

Related Articles 15

Recommended Articles

Metrics

场景数据	ST		TRS
场景数据	RF	SVM（Linear）	RF	SVM（Linear）
ECG200	0.830	0.810	0.950	0.890
ECG5000	0.944	0.932	0.951	0.948
ECGFiveDays	0.933	0.990	1.000	1.000
NonInvasiveFatalECGThorax1	0.950	0.877	0.955	0.958
NonInvasiveFatalECGThorax2	0.951	0.938	0.969	0.967
TwoLeadECG	0.961	0.993	0.978	0.972
CinECGTorso	0.859	0.901	0.954	0.901
Lightning7	0.726	0.712	0.767	0.780
MoteStrain	0.846	0.886	0.939	0.907
Phoneme	0.321	0.321	0.361	0.369
Plane	1.000	1.000	1.000	1.000
SonyAIBORobotSurface1	0.851	0.867	0.965	0.965
SonyAIBORobotSurface2	0.934	0.937	0.929	0.938
Wafer	1.000	1.000	0.999	0.999
Average Accuracy	0.865	0.869	0.908	0.900
Average Rank	2.920	2.643	1.780	1.780
Wilcoxon Test p value	0.003	0.012	—	—

数据集	无处理	关键点剪枝	关键点剪枝&AMP剪枝
ECG200	0.695±0.012	0.878±0.006	0.934±0.020
ECG5000	0.844±0.030	0.922±0.005	0.948±0.003
ECGFiveDays	0.813±0.001	0.998±0.000	1.000±0.000
NonInvasiveFatalECGThorax1	0.853±0.002	0.931±0.008	0.943±0.013
NonInvasiveFatalECGThorax2	0.772±0.002	0.924±0.012	0.961±0.010
TwoLeadECG	0.893±0.004	0.951±0.004	0.996±0.001
CinECGTorso	0.724±0.001	0.860±0.022	0.901±0.033

数据集	TRS		ST
数据集	带位置信息关键形态表征	不带位置信息关键形态表征	ST
ECG200	0.950	0.890	0.830
ECG5000	0.951	0.928	0.944
ECGFiveDays	1.000	0.954	0.933
NonInvasiveFatalECGThorax1	0.955	0.952	0.950
NonInvasiveFatalECGThorax2	0.969	0.956	0.951
TwoLeadECG	0.997	0.977	0.961
CinECGTorso	0.901	0.900	0.859

[1]	Hanlin ZHANG, Junlu WANG, Baoyan SONG. Time series event classification method fused with derived features [J]. Journal of Computer Applications, 2025, 45(2): 428-435.
[2]	Siqi ZHANG, Jinjun ZHANG, Tianyi WANG, Xiaolin QIN. Deep temporal event detection algorithm based on signal temporal logic [J]. Journal of Computer Applications, 2025, 45(1): 90-97.
[3]	Zidong CHENG, Peng LI, Feng ZHU. Potential relation mining in internet of things threat intelligence knowledge graph [J]. Journal of Computer Applications, 2025, 45(1): 24-31.
[4]	Jianpeng HU, Lichen ZHANG. Deep spatio-temporal network model for multi-time step wind power prediction [J]. Journal of Computer Applications, 2025, 45(1): 98-105.
[5]	Zijun MIAO, Fei LUO, Weichao DING, Wenbo DONG. Traffic signal control algorithm based on overall state prediction and fair experience replay [J]. Journal of Computer Applications, 2025, 45(1): 337-344.
[6]	Wenbo ZHAO, Zitong MA, Zhe YANG. Link prediction model based on directed hypergraph adaptive convolution [J]. Journal of Computer Applications, 2025, 45(1): 15-23.
[7]	Qinzhuang ZHAO, Hongye TAN. Time series causal inference method based on adaptive threshold learning [J]. Journal of Computer Applications, 2024, 44(9): 2660-2666.
[8]	Jieru JIA, Jianchao YANG, Shuorui ZHANG, Tao YAN, Bin CHEN. Unsupervised person re-identification based on self-distilled vision Transformer [J]. Journal of Computer Applications, 2024, 44(9): 2893-2902.
[9]	Liting LI, Bei HUA, Ruozhou HE, Kuang XU. Multivariate time series prediction model based on decoupled attention mechanism [J]. Journal of Computer Applications, 2024, 44(9): 2732-2738.
[10]	Shunyong LI, Shiyi LI, Rui XU, Xingwang ZHAO. Incomplete multi-view clustering algorithm based on self-attention fusion [J]. Journal of Computer Applications, 2024, 44(9): 2696-2703.
[11]	Yu DU, Yan ZHU. Constructing pre-trained dynamic graph neural network to predict disappearance of academic cooperation behavior [J]. Journal of Computer Applications, 2024, 44(9): 2726-2731.
[12]	Lilin FAN, Fukang CAO, Wanting WANG, Kai YANG, Zhaoyu SONG. Intermittent demand forecasting method based on adaptive matching of demand patterns [J]. Journal of Computer Applications, 2024, 44(9): 2747-2755.
[13]	Tingjie TANG, Jiajin HUANG, Jin QIN, Hui LU. Session-based recommendation based on graph co-occurrence enhanced multi-layer perceptron [J]. Journal of Computer Applications, 2024, 44(8): 2357-2364.
[14]	Yike HAN, Bin XU, Shuo ZHANG. Personalized exercise recommendation based on cognitive diagnosis [J]. Journal of Computer Applications, 2024, 44(8): 2351-2356.
[15]	Yuan TANG, Yanping CHEN, Ying HU, Ruizhang HUANG, Yongbin QIN. Relation extraction model based on multi-scale hybrid attention convolutional neural networks [J]. Journal of Computer Applications, 2024, 44(7): 2011-2017.