Graphical time warping for joint alignment of multiple curves

Yizhi Wang, David J. Miller, Kira Poskanzer, Yue Wang, Lin Tian, Guoqiang Yu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function. However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often related, independent application of DTW to each pair is a sub-optimal solution. Yet, it is largely unknown how to efficiently conduct a joint alignment with all warping functions simultaneously considered, since any given warping function is constrained by the others and dynamic programming cannot be applied. In this paper, we show that the joint alignment problem can be transformed into a network flow problem and thus can be exactly and efficiently solved by the max flow algorithm, with a guarantee of global optimality. We name the proposed approach graphical time warping (GTW), emphasizing the graphical nature of the solution and that the dependency structure of the warping functions can be represented by a graph. Modifications of DTW, such as windowing and weighting, are readily derivable within GTW. We also discuss optimal tuning of parameters and hyperparameters in GTW. We illustrate the power of GTW using both synthetic data and a real case study of an astrocyte calcium movie.

Original languageEnglish (US)
Pages (from-to)3655-3663
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - 2016

Fingerprint

Time series analysis
Dynamic programming
Calcium
Tuning
Metabolomics
Astrocytes

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Wang, Y., Miller, D. J., Poskanzer, K., Wang, Y., Tian, L., & Yu, G. (2016). Graphical time warping for joint alignment of multiple curves. Advances in Neural Information Processing Systems, 3655-3663.

Graphical time warping for joint alignment of multiple curves. / Wang, Yizhi; Miller, David J.; Poskanzer, Kira; Wang, Yue; Tian, Lin; Yu, Guoqiang.

In: Advances in Neural Information Processing Systems, 2016, p. 3655-3663.

Research output: Contribution to journalArticle

Wang, Yizhi ; Miller, David J. ; Poskanzer, Kira ; Wang, Yue ; Tian, Lin ; Yu, Guoqiang. / Graphical time warping for joint alignment of multiple curves. In: Advances in Neural Information Processing Systems. 2016 ; pp. 3655-3663.
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