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I'm doing an experiment where a user tries to draw a shown trajectory.

So, we have two trajectories - one 'template' trajectory with a fixed number of elements (3d coordinates) and a trajectory with an arbitrary number of elements (3d coordinates) drawn by a user. The templates are simple shapes such as a circle, a triangle and a square.

I'd like to compare/analyze the two trajectories and so far I've come up with what I think are subpar (and simple) ways to compare the two:

  1. Compare the centroid (the mean) of the trajectories
  2. Compare the extremities of each dimension

While this can be accurate when the two shapes are similar, it can also show 'false positives' when the shapes are completely dissimilar but have similar metrics. I cannot compare pair-wise since the user generated trajectory does not have a static fixed number of elements (or can I?).

Any input or thoughts would be appreciated. Not sure what to add as a tag so I'll just add correlation...

Space
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  • Welcome to Cross Validated! This sounds like something called functional data analysis (FDA). Perhaps look into FDA and see if that works for your task. – Dave Jun 11 '22 at 14:37
  • You will get ideas from https://stats.stackexchange.com/questions/27861/similarity-measures-between-curves, https://stats.stackexchange.com/questions/236556/similarity-between-time-dependent-paths – kjetil b halvorsen Jun 11 '22 at 20:09

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