quantitative measure of similarity of curves

Frank Chang — Tue, 03 Nov 2009 18:08:10 -0500

Hi Group,

I am not sure if this is the appropriate newsgroup to post this
question. But I feel like we have people with all kinds of expertise
here. So I am giving it a try.

Let's assume we have many curves which are similar to each other
(measurement taken at different times). These curves stabilize over
time (i.e., fluctuate more at the beginning of the sequence, less in
the end). I'd like to find a quantitative measure to characterize
this. So far, I tried a "variance" parameter defined as the following

V = sqrt(1/N sum_j(log(Yi, j) - log(Yi+1, j))),

where Yi, j is the jth data point of the ith measurement. N is the
number of data points in each measurement, and Yi,j is real positive.

For some reason, this measure does not characterize the stabilization
process well. I am sure there is some statistical measure out there
which is better than this crude calculation. I'd be grateful if you
could please offer your insights.

Thanks!

Frank

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quantitative measure of similarity of curves