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I am working with a MRI dataset where we inject dye into a person's wrist and measure intensity per time on a voxel-by-voxel basis. I am trying to determine if it is possible to identify certain tissues based upon their curve similarity (they have unique looking intensity curves).

one example curve

I am using Euclidean distance k-means in order to try this. The data seems to be OK, but I need a way to determine uniformity between curves—how similar curves in a group are to one another. Any suggestions on how to do this?

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    $\begingroup$ Can you provide some example data? What are the "curves" in this context? Are they some kind of densities over values (eg, histograms)? Are they curvilinear relationships b/t 2 different variables? $\endgroup$
    – gung - Reinstate Monica
    Commented Aug 1, 2017 at 18:47
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    $\begingroup$ It is intensity over time. So, for a specific voxel, I would have one intensity value per one time point. $\endgroup$
    – Sameer Khanna
    Commented Aug 1, 2017 at 18:48
  • $\begingroup$ Here is an example of what a curve might look like. link $\endgroup$
    – Sameer Khanna
    Commented Aug 1, 2017 at 18:52
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    $\begingroup$ How many curves do you have? Are you trying to cluster (unsupervised) or build a classification model that correctly identifies labeled and unlabeled cases? $\endgroup$
    – Ben
    Commented Aug 2, 2017 at 21:00
  • $\begingroup$ What is important for you in measuring similarity of curves? only the values? derivatives? Something else? This curves can be seen as functions, so some possibilities are: $L_1$, $L_2$, or using derivatives some Sobolev space distance $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jan 17, 2019 at 9:31

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