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I am attempting to estimate the similarity between three different entities (here expressed as curves). One of the curves represent a "teacher" (green curve) and the other two are "students".

While researching how to solve this problem, I have come across multiple techniques:

All three methods have their own advantages and disadvantages, however neither of them seem to help me with the problem demonstrated in the image:

  • I "know" that "student 3" (orange curve) is closer to the "teacher", however distance wise "student 5" is measured as closest one

  • Peak estimations works well for sharp edges, and it does not perform well here.

Three curves for estimating their similarity

I do not have a background in signal processing (which is what the problem appears to be requiring), and I would appreciate general suggestions/techniques on how to address these types of problems.

Community
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Snejana Shegheva
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This problem isn't necessarily related to signal processing but to curve fitting or optimization in general. When you say that student 3 is "closer", you have to define "closeness".When using pre-defined distance function like you did, you have arbitrarily chosen a distance measure which isn't necessarily suitable to your needs.Estimating from the drawing, I think that by using Euclidean distance you'll get what you want (that student 3 is closer).

Gabizon
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  • Thanks @Gabe. I am using a generalized euclidian distance - minkowski distance. I am going to run through the results again, but I think it didn't give me what I wanted which I why I started to look at peak analysis (I am glad I do not need signal processing here yet and this problem is solvable with distance measure) – Snejana Shegheva Jul 25 '16 at 21:35
  • Yes, indeed - Euclidian distance (or minkowski with p=2) works fine here. I must have been looking at a different instance of the curves at a time. – Snejana Shegheva Jul 26 '16 at 00:14