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

William Simpson william.a.simpson at gmail.com
Mon Aug 31 15:15:24 CEST 2009

```Thanks Chuck. Interesting suggestion.

Thanks to everyone for the help.

Bill

On Sun, Aug 30, 2009 at 4:59 PM, Charles C. Berry<cberry at tajo.ucsd.edu> wrote:
>
>
> Bill,
>
>        prod( cancor( A,B )\$cor )
>
> perhaps?
>
> Note that this accounts for linear transformations.
>
> HTH,
>
> Chuck
>
> On Sun, 30 Aug 2009, 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
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> Charles C. Berry                            (858) 534-2098
>                                            Dept of Family/Preventive
> Medicine
> E mailto:cberry at tajo.ucsd.edu               UC San Diego
> http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901
>
>
>

```