# Clustering a set of curves

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).

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?

• 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? – gung - Reinstate Monica Aug 1 '17 at 18:47
• It is intensity over time. So, for a specific voxel, I would have one intensity value per one time point. – Sameer Khanna Aug 1 '17 at 18:48
• Here is an example of what a curve might look like. link – Sameer Khanna Aug 1 '17 at 18:52
• How many curves do you have? Are you trying to cluster (unsupervised) or build a classification model that correctly identifies labeled and unlabeled cases? – Ben Aug 2 '17 at 21:00
• 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 – kjetil b halvorsen Jan 17 '19 at 9:31