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I have two curves extracted from some data and I'm trying to detect when there is a difference. Each of these 3 plots represents a different data set.

From these example curves below, I'm looking for a metric that I can use to compare the green and blue plots. These are normalised plots.

The Left and Right plots are examples of a matching case. The middle plot is an example of non-matching data set.

I've tried using Chi-Square and Bhattacharyya distance but neither give good separation between data sets.

Any suggestions?

enter image description here

YMDW
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1 Answers1

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Given that these are curves of the form $y=f(x)$, i.e., graphs of some functions, you can use one of popular norms on function spaces, such as:

  • uniform norm $\max_{a\le x\le b} |f(x)-g(x)|$
  • $L^1$ norm $\int_a^b |f(x)-g(x)|\,dx$
  • $L^2$ norm $\int_a^b |f(x)-g(x)|^2\,dx$

(Integrals become sums for discrete data).

I would probably go with $L^2$ distance, which from the appearance of the curves should be substantially larger for the plot in the middle.