mlpy - Dynamic Time Warping depends on x?

Question

I am trying to get the distance between these two arrays shown below by DTW.

Answer 1

Let me reiterate what I have understood, please correct me if I am going wrong anywhere. I observe that in both your plots, your 1D series in blue is remaining identical, while green colored is getting stretched. How you are doing it, that you have explained it in the post on Sep 19 '13 at 9:36. Your premise is that because (1) DTW 'takes care' of time shift and (2) all that you are doing is stretching one time-series length-wise, not affecting y-values, (Inference:) you are expecting distance to remain the same.

There is a little missing link between [(1),(2)] and [(Inference)]. Which is, individual distance values corresponding to mappings WILL change as you change set of signals itself. And this will result into difference in the overall distance computation. Plot the warping paths, cost grid to see it for yourself.

Let's take an oversimplified case...

Let a=range(0,101,5) = [0,5,10,15...95, 100]

and b=range(0,101,5) = [0,5,10,15...95, 100].

Now intuitively speaking, you/I would expect one to one correspondence between 2 signals (for DTW mapping), and distance for all of the mappings to be 0, signals being identically looking.

Now if we make, b=range(0,101,4) = [0,4,8,12...96,100], DTW mapping between a and b still would start with a's 0 getting mapped to b's 0, and end at a's 100 getting mapped to b's 100 (boundary constraints). Also, because DTW 'takes care' of time shift, I would also expect 20's, 40's, 60's and 80's of the two signals to be mapped with one another. (I haven't tried DTWing these two myself, saying it from intuition, so please check. There is little possibility of non-intuitive warpings taking place as well, depending on step patterns allowed / global constraints, but let's go with intuitive warpings for the moment for the ease of understanding / sake of simplicity).

For the remaining data points, clearly, distances corresponding to mapping are now non-zero, therefore the overall distance too is non-zero. Our distance/overall cost value has changed from zero to something that is non-zero.

Now, this was the case when our signals were too simplistic, linearly increasing. Imagine the variabilities that will come into picture when you have real life non-monotonous signals, and need to find time-warping between them. :)

(PS: Please don't forget to upvote answer :D). Thanks.