W-tss: A wavelet-based algorithm for discovering time series shapelets

Kenan Li, Huiyu Deng, John Morrison, Rima Habre, Meredith Franklin, Yao Yi Chiang, Katherine Sward, Frank D. Gilliland, José Luis Ambite, Sandrah P. Eckel

Research output: Contribution to journalArticlepeer-review


Many approaches to time series classification rely on machine learning methods. However, there is growing interest in going beyond black box prediction models to understand discriminatory features of the time series and their associations with outcomes. One promising method is time-series shapelets (TSS), which identifies maximally discriminative subsequences of time series. For example, in environmental health applications TSS could be used to identify short-term patterns in exposure time series (shapelets) associated with adverse health outcomes. Identification of candidate shapelets in TSS is computationally intensive. The original TSS algorithm used exhaustive search. Subsequent algorithms introduced efficiencies by trimming/aggregating the set of candidates or training candidates from initialized values, but these approaches have limitations. In this paper, we introduce Wavelet-TSS (W-TSS) a novel intelligent method for identifying candidate shapelets in TSS using wavelet transformation discovery. We tested W-TSS on two datasets: (1) a synthetic example used in previous TSS studies and (2) a panel study relating exposures from residential air pollution sensors to symptoms in participants with asthma. Compared to previous TSS algorithms, W-TSS was more computationally efficient, more accurate, and was able to discover more discriminative shapelets. W-TSS does not require pre-specification of shapelet length.

Original languageEnglish (US)
Article number5801
Issue number17
StatePublished - Sep 2021

Bibliographical note

Funding Information:
Funding: Please add: This research was funded by NIH/NIBIB (National Institutes of Health/National Institute of Biomedical Imaging and Bioengineering), grant number (1) U24EB021996, (2) U54EB021973, (3) U54EB022002, and NIEHS (National Institute of Environmental Health Sciences), grant number (4) R01ES027860 Institutional Review Board Statement: This study was carried out in consent with all the relevant guidelines and regulations by the University of Utah and the University of Southern California. All methods and experimental protocols were reviewed and approved by the Institutional Review Boards (IRBs).

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.


  • Pattern discovery
  • Shapelets
  • Time series classification
  • Time series mining
  • Wavelets


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