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I would like to visualize a large amount of events composed of time serie windows. A typical event would be:

typical event

Problem is, my events are not synchronized, and so if I plot them all, it would look like:

enter image description here

Question
Is there any way to visualize all my events so I can see their original/"typical" shape (preferably in the time domain) despite their unsynchronization ?

What I have tried so far:

  • Visualize features: approach is good but I have to guess what I am looking for.
  • Synchronized events: in the example above it might be possible, but for some other cases it won't be. (such as multiple peaks spaced with different time lapses)
  • Use statistical values to visualize: that was my first shot, to plot not all events but only their mean, median, p95,... Problem is, using this approach gives a deformed rendering of the data because of the unsynchronization:

enter image description here

What I have thought about

The main problem of applying the mean, p95 or whatever statistical function is that it is applied along an axis that is not synchronized between events. I don't know if it exists or if it is even feasible, but I was thinking about an approach that would display those statistical values checking their temporal neighbors ? I know Dynamic Time Warping deals with this unsynchronization but I am not sure if and how I could use it to plot my events in the way I'd like.
An idea of a possible output could be (any other output idea is welcomed!):

enter image description here

Any help, idea, would be greatly appreciated ! Thanks

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    $\begingroup$ DTW is a good solution for this problem. This post might help you ealizadeh.com/blog/introduction-to-dynamic-time-warping $\endgroup$
    – WBM
    Feb 26, 2021 at 10:39
  • $\begingroup$ Thanks @WBM, how would you do use DTW to display a graph like the last one ? Have you seen raw data visualization based on DTW ? $\endgroup$
    – etiennedm
    Feb 26, 2021 at 10:43
  • $\begingroup$ So you use DTW to cluster the clips in time (or warp them so they're aligned) and then you create an average of those clusters which would be your ideal_sig in the final image $\endgroup$
    – WBM
    Feb 26, 2021 at 10:46
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    $\begingroup$ Thanks, I think I see your point, I will dig into it and try to build a function that does that $\endgroup$
    – etiennedm
    Feb 26, 2021 at 11:20

1 Answer 1

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As far as estimating similarity between the time series series there is a variety of methods you may want to investigate. Some of those are:

  • cross correlation: this will be affected by the amplitude and will not be able to estimate lagged correlations, prone to noise.
  • coherence: normalised frequency based correlation (cross-spectrum), not prone to amplitude or noise.
  • wavelet coherence: similar to above but based on wavelet transformations instead of STFFT.
  • dynamic time warping: measuring similarity between two temporal sequences, which may vary in speed.
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  • $\begingroup$ Thanks @hH1sG0n3, I am looking for a tool that precedes the investigation of similarities, a tool that could point me where to look for similarities into a large amount of data by visualizing them in a specific way. I don't know if such a tool/plot exists or if as you proposed, I have to directly dig into all possible features that extract similarities. $\endgroup$
    – etiennedm
    Feb 26, 2021 at 11:24
  • $\begingroup$ Coherency metrics can be calculated across multiple events. I thought this may be useful since this can be considered an event related analysis? $\endgroup$
    – hH1sG0n3
    Feb 26, 2021 at 12:47
  • $\begingroup$ Yes, definitely it is related, thanks. But I am looking for a way to visualize all my events so I can see their original shape (preferably in the time domain) despite their unsynchronization. The example I have used is simplified and in the real case I have no clue about the shape. I think I know how to use your metrics and as they are, I don't think any directly achieve what I am looking for, do they ? Sorry if it wasn't clear in the question. $\endgroup$
    – etiennedm
    Feb 27, 2021 at 9:09
  • $\begingroup$ I have updated the question, I hope it is more clear now $\endgroup$
    – etiennedm
    Feb 27, 2021 at 9:13

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