Abstract
Deep neural networks (DNNs) have shown remarkable performance in time series classification tasks. However, the DNNs rely on a mass of data, which may not accumulate in real scenarios. As such, researchers investigate data augmentation methods to solve the scarcity of labeled data. Some of them, such as the rotation, that borrowed from the computer vision are not applicable due to the unique property of time series data. Besides, existing frequency-based methods applied for audio and speech recognition generate new samples by changing original frequency information, which may introduce unreasonable variation. In this paper, we propose a novel time series data augmentation method called Stratified Fourier Coefficients Combination (SFCC). SFCC retains and combines the original Fourier coefficients to augment the time series datasets. First, we transform data into the frequency domain using the discrete Fourier transform (DFT). To maintain the initial data distribution, we stratify the coefficients into several groups and then randomly select the groups to concatenate the coefficients. Finally, a new sample is generated through inverse DFT. The experiments demonstrate that the augmentation by SFCC can effectively improve the performance of the DNNs and achieve state-of-the-art results compared with the other 12 benchmarking methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Euler’s formula \(e^{ix} = \cos x + i\sin x\).
The source code of SFCC and more experimental results could be found on our supporting website https://sites.google.com/view/sfcc-supply.
References
Ma H, Li W, Zhang X, Gao S, Lu S (2019) Attnsense: multi-level attention mechanism for multimodal human activity recognition. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI-19, pp 3109–3115
Fawaz HI, Forestier G, Weber J, Idoumghar L, Muller P-A (2019) Deep learning for time series classification: a review. Data Min Knowl Disc 33(4):917–963
Torralba A, Fergus R, Freeman WT (2008) 80 million tiny images: a large data set for nonparametric object and scene recognition. IEEE Trans Pattern Anal Mach Intell 30(11):1958–1970
Der Maaten LV, Hinton GE (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579–2605
Iwana BK, Uchida S (2020) An empirical survey of data augmentation for time series classification with neural networks. arXiv e-prints, 2007–15951
Um TT, Pfister FMJ, Pichler D, Endo S, Lang M, Hirche S, Fietzek U, Kulić D (2017) Data augmentation of wearable sensor data for parkinson’s disease monitoring using convolutional neural networks. In: Proceedings of the 19th ACM International Conference on Multimodal Interaction. ICMI ’17, pp. 216–220
Le Guennec A, Malinowski S, Tavenard R (2016) Data augmentation for time series classification using convolutional neural networks. In: ECML/PKDD Workshop on Advanced Analytics and Learning on Temporal Data
Bishop CM (1995) Training with noise is equivalent to tikhonov regularization. Neural Comput 7(1):108–116
Simonyan K, Zisserman A (2015) Very deep convolutional networks for large-scale image recognition. In: International Conference on Learning Representations, ICLR 2015
Petitjean F, Ketterlin A, Gançarski P (2011) A global averaging method for dynamic time warping, with applications to clustering. Pattern Recogn 44(3):678–693
Iwana BK, Seiichi U (2020) Time series data augmentation for neural networks by time warping with a discriminative teacher. arXiv e-prints, 2004–08780
Jaitly N, Hinton GE (2013) Vocal tract length perturbation (vtlp) improves speech recognition. In: Proc. ICML Workshop on Deep Learning for Audio, Speech and Language, vol. 117
Meng X, Su J, Wang Y (2002) Data reduction and noise filtering for predicting. Lect Notes Comput Sci 2419(Chapter 39):421–429
Deng J, Chen X, Jiang R, Song X, Tsang IW (2021) St-norm: Spatial and temporal normalization for multi-variate time series forecasting. In: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp. 269–278
Wu Z, Yu H, Chen CW (2010) A new hybrid dct-wiener-based interpolation scheme for video intra frame up-sampling. IEEE Signal Process Lett 17(10):827–830
Forestier G, Petitjean F, Dau HA, Webb GI (2017) Keogh: Generating synthetic time series to augment sparse datasets. In: 2017 IEEE International Conference on Data Mining (ICDM), pp. 865–870
Gao J, Song X, Wen Q, Wang P, Sun L, Xu H (2020) Robusttad: robust time series anomaly detection via decomposition and convolutional neural networks. arXiv preprint, 2002–09545
Steven Eyobu O, Han DS (2018) Feature representation and data augmentation for human activity classification based on wearable imu sensor data using a deep lstm neural network. Sensors 18(9):2892
Takahashi N, Gygli M, Pfister B, Gool LV (2016) Deep convolutional neural networks and data augmentation for acoustic event recognition. In: Interspeech 2016, pp. 2982–2986
Lee TEKM, Kuah YL, Leo K, Sanei S, Chew E, Zhao L (2019) Surrogate rehabilitative time series data for image-based deep learning. In: 2019 27th European Signal Processing Conference (EUSIPCO), pp. 1–5
Yoon J, Jarrett D, Schaar MVD (2019) Time-series generative adversarial networks. In: Neural Information Processing Systems (NeurIPS)
Wen Q, Sun L, Song X, Gao J, Wang X, Xu H (2020) Time series data augmentation for deep learning: a survey. arXiv e-prints, 2002–12478
Dau HA, Bagnall A, Kamgar K, Yeh C-CM, Zhu Y, Gharghabi S, Ratanamahatana CA, Keogh E (2019) The ucr time series archive. IEEE/CAA J Automatica Sin 6(6):1293–1305
Wang Z, Yan W, Oates T (2017) Time series classification from scratch with deep neural networks: A strong baseline. In: 2017 International Joint Conference on Neural Networks (IJCNN), pp. 1578–1585
Rashid KM, Louis J (2019) Time-warping: a time series data augmentation of imu data for construction equipment activity identification. In: 36th International Symposium on Automation and Robotics in Construction
Kamycki K, Kapuscinski T, Oszust M (2020) Data augmentation with suboptimal warping for time-series classification. Sensors 20(1):98
Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30
Benavoli A, Corani G, Demšar J, Zaffalon M (2017) Time for a change: a tutorial for comparing multiple classifiers through bayesian analysis. J Mach Learn Res 18(1):2653–2688
Brigham EO, Morrow RE (1967) The fast fourier transform. IEEE Spectr 4(12):63–70
Acknowledgements
This work is supported by National Key R &D Program of China (2021ZD0113002), Beijing Natural Science Foundation (4214067) and Fundamental Research Funds for the Central Universities (KKJBMC22006536).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yang, W., Yuan, J. & Wang, X. SFCC: Data Augmentation with Stratified Fourier Coefficients Combination for Time Series Classification. Neural Process Lett 55, 1833–1846 (2023). https://doi.org/10.1007/s11063-022-10965-9
Accepted:
Published:
Version of record:
Issue date:
DOI: https://doi.org/10.1007/s11063-022-10965-9