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I have two arrays of 2D points and I need to estimate their correlation. What formula should I use?

Example of arrays:

$$X: ((1,5),(2,5),(1,7),(4,1)),$$

$$Y: ((3,4),(1,6),(4,6),(4,3)).$$

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    $\begingroup$ A reference is Tobler, W.R. 1965. Computation of the correspondence of geographical patterns. Papers in Regional Science 15: 131–139. doi: 10.1111/j.1435-5597.1965.tb01318.x $\endgroup$
    – Nick Cox
    Oct 26, 2013 at 0:12
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    $\begingroup$ Another reference (much more recent and accessible) jstatsoft.org/v52/c01/paper $\endgroup$
    – Nick Cox
    Oct 26, 2013 at 0:36
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    $\begingroup$ Brownian correlation? It can be computed between arrays of any, even different dimensionality. $\endgroup$
    – ttnphns
    Oct 26, 2013 at 6:12
  • $\begingroup$ Thank you for your replies! As for now I started trying Brownian correlation and RV coefficient. The coefficient from Tobler (if I understood correctly) is not symmetrical and it seems like a disadvantage for me, so I didn't try it. $\endgroup$ Oct 26, 2013 at 20:30
  • $\begingroup$ Why not distance covariance or distance correlation? en.wikipedia.org/wiki/Distance_correlation#Distance_covariance $\endgroup$ Aug 24, 2016 at 6:35

1 Answer 1

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The Pyramid Match Kernel is a flexible technique for estimating a normalized correspondence strength between multidimensional point sets. It is analogous to $R^2$ in many ways (symmetric, values in $[0,1]$), and could suit your purposes.

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