# [R] correlation between two 2D point patterns?

Bernardo Rangel Tura tura at centroin.com.br
Sun Aug 30 11:46:08 CEST 2009

```On Sun, 2009-08-30 at 07:51 +0100, William Simpson wrote:
> Suppose I have two sets of (x,y) points like this:
>
> x1<-runif(n=10)
> y1<-runif(n=10)
> A<-cbind(x1,y1)
>
> x2<-runif(n=10)
> y2<-runif(n=10)
> B<-cbind(x2,y2)
>
> I would like to measure how similar the two sets of points are.
> Something like a correlation coefficient, where 0 means the two
> patterns are unrelated, and 1 means they are identical. And in
> addition I'd like to be able to assign a p-value to the calculated
> statistic.
>
> cor(x1,x2)
> cor(y1,y2)
> gives two numbers instead of one.
>
> cor(A,B)
> gives a correlation matrix
>
> I have looked a little at spatial statistics. I have seen methods
> that, for each point, search in some neighbourhood around it and then
> compute the correlation as a function of search radius. That is not
> what I am looking for. I would like a single number that summarises
> the strength of the relationship between the two patterns.
>
> I will do procrustes on the two point sets first, so that if A is just
> a rotated, translated, scaled, reflected version of B the two patterns
> will superimpose and the statistic I'm looking for will say there is
> perfect correspondence.
>
> Thanks very much for any help in finding such a statistic and
> calculating it using R.
>
> Bill

Hi Bill,

If your 2 points set is similar I expect your Euclidean distance is 0,
so I suggest this script:

dist<-sqrt((x1-x2)^2+(y1-y2)^2) # Euclidean distance

t.test(dist) # test for mean equal 0

--
Bernardo Rangel Tura, M.D,MPH,Ph.D
National Institute of Cardiology
Brazil

```