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I have time series of different lengths with different patterns. I want to find the similarity between them in such a way that it is defined from 0 to 1 and the measure takes into account the length (of time). I decided to use cosine similarity as a metric (I also read about DTW, but I have different waveforms possible). However, I do not want to use resampling to bring the signals to the same length and I want the similarity to decrease with the difference in length. That is, the measure should describe the similarity of forms and the difference in time. Help if anyone came across this!

Example: enter image description here

In this example, it is important for me what in first signal the duration is 80 seconds, and in the second 200 seconds, and I want this to affect the similarity.

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    $\begingroup$ What is your data? Could you give some examples? $\endgroup$
    – Tim
    Commented Sep 6, 2021 at 19:25
  • $\begingroup$ Okay, I added one example. $\endgroup$
    – SoH
    Commented Sep 6, 2021 at 19:53
  • $\begingroup$ Most of many (dis)similarity measures, including cosine sim., come from the assumption that there is a instance by instance correspondence bw the two vectors. That is, vector (a1, a2, a3, a4) and vector (b1, b2, b3, b4) have fixed pairs to compare within: a1 vs b1, a2 vs b2,... Do you think this idea of preset pairs is suitable in your situation. Does time t2 (say) in one series is the same as time t2 inanother series? $\endgroup$
    – ttnphns
    Commented Sep 7, 2021 at 10:28
  • $\begingroup$ Also, make a search on the site, "similarities vectors different length" $\endgroup$
    – ttnphns
    Commented Sep 7, 2021 at 10:34
  • $\begingroup$ @ttnphns Yes, I think the time is the same. Each time series is the same process that lasts for different times. $\endgroup$
    – SoH
    Commented Sep 7, 2021 at 18:06

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