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I'm looking into the Itakura Parallelogram global constraint for Dynamic Time Warping.

I am confused about the maximum width of the parallelogram, is it solely based on the length of the two time series being compared, or can it be varied to achieve a bigger or smaller warping window?

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The maximum width (or the length of the smaller diagonal) of the paralelogram is implicitly dependent on the maximum allowed delay (or distance), around the middle of the signal. In this example figure (taken from here), the maximum allowed delay is $dt=4$ and hence the length of the diagonal is $\sqrt{2} dt = 5.66$.

If you take that (maximum allowed delay) as parameter, the absolute width of the paralelogram does not change when the series length change. However, you could instead take as fixed parameter the slope of the paralelogram sides (which would be equivalent to impose a maximum "speed change" between the two signals). In this case, the shape of the paralelogram would not change with the series length, and the size of the smaller diagonal woul be proportional on the series length.

enter image description here

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  • $\begingroup$ Does this mean I could alter the maximum allowed delay? So for the example figure could I set dt=6, so that I would have a wider parallelogram in the middle? Or for that example does dt always equal 4? $\endgroup$ – Chris Apr 10 '12 at 14:27
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    $\begingroup$ @Chris: you can change the maximum allowed delay (as in the Sakoe/Chiba bands) as you like $\endgroup$ – leonbloy Apr 10 '12 at 14:41
  • $\begingroup$ thanks for the clarification. I was just looking at the R implementation of Itakura Parallelogram and it has no way of setting max allowed delay, so it threw me off because I had assumed you could alter it. $\endgroup$ – Chris Apr 10 '12 at 14:48

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