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R version 2.9.2 (2009-08-24)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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>
> d1 = c(3,2,0,5,0,0,0,2,0,0)
> d2 = c(1,0,0,0,0,0,0,1,0,2)
>
> # our cosine similarity function
>
> cos.sim = function(p,q) {
+
+ return(sum(p*q) / sqrt(sum(p^2)*sum(q^2)))
+
+ }
>
> print(cos.sim(d1,d2))
[1] 0.3149704
>
> # cosine similarity is not exactly the same
> # as correlation
>
> print(cor(d1,d2))
[1] 0.01814885
>
> # but, correlation is the same as cosine similarity
> # after removing the mean
>
> print(cos.sim(d1-mean(d1),d2-mean(d2)))
[1] 0.01814885
>
> # other measures of correlation
> # Spearman, Kendall uses ranks of the data
>
> print(cor(d1, d2, method='kendall'))
[1] 0.1936008
> print(cor(d1, d2, method='spearman'))
[1] 0.2160396
>
>
>
>
> # here is a generative example of correlation
> # that reproduces a plot similar to the notes
>
> correlated.data = function(n=50, rho=0) {
+ x = rnorm(n)
+ y = rho*x + sqrt(1-rho^2)*rnorm(n)
+ return(data.frame(x,y))
+ }
>
> rho = seq(-1,1,length=9)
> par(mfrow=c(3,3))
>
> for (r in rho) {
+ d = correlated.data(rho=r)
+ plot(d, main=r)
+ }
>
>
>

>
> proc.time()
user system elapsed
0.636 0.028 0.806
R script