Solved – Dynamic Time Warping for irregular time series

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I have been reading a lot about Dynamic Time Warping (DTW) lately. I am very surprised that there is no literature at all on the application of DTW to irregular time series, or at least I could not find it.

Could anybody give me a reference to something related to that issue, or maybe even an implementation of it?

Best Answer

As far as I understand, by irregular time series you mean unevenly spaced time series, also referred to as irregularly sampled time series. Since I am curious about time series in general, I have performed a brief research on the topic of your (and now mine) interest. The results follow.

Despite high popularity of dynamic time warping (DTW) approach in time series analysis, clustering and classification, irregular time series present some challenges to direct application of DTW to such data type (for example, see this paper and this paper). Based on my relatively brief research efforts, it is not totally clear to me, whether it is impossible to apply DTW directly, as some research suggests otherwise (also see this paper/chapter). For more comprehensiveness, I also would like to mention an IMHO excellent and relevant to the topic dissertation on irregular time series.

Nevertheless, it seems that this topic is mostly covered by the following two research streams:

  • proposing and evaluating approaches, alternative to DTW, such as model-based ones (see this paper and this paper);
  • proposing and evaluating modified DTW approaches, such as cDTW, EDR, ERP, TWED, envelope transforms, CDTW (continuous DTW - do not confuse with cDTW - constrained DTW!) and others variants (for example, see this paper). An overview of the above-mentioned approaches and results of some empirical comparisons can be found in this paper.

Finally, I would like to touch on the subject of open source software, available for research or system implementation, focused on DTW and supporting some of the above-mentioned algorithms for irregular time series. Such software include Python/NumPy-based cDTW module project as well as GPU-focused CUDA-based CUDA-DTW project. For R enthusiasts, a comprehensive Dynamic Time Warp project also should be mentioned (corresponding package dtw is available on CRAN). Even though it might not support many DTW algorithms for irregular time series at the moment (though I think it supports cDTW), I think it is just a matter of time until this project will offer more comprehensive support for DTW algorithms, focused on such type of data. I hope that you have enjoyed reading my answer as much as I have enjoyed researching the topic and writing this post.

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