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 journalConference articlepeer-review

    6 Scopus citations


    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 - Jan 1 2016
    Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
    Duration: Dec 5 2016Dec 10 2016

    All Science Journal Classification (ASJC) codes

    • Computer Networks and Communications
    • Information Systems
    • Signal Processing


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