Compute a cosine dissimilarity matrix in R

Question

I want to create heatmaps based upon cosine dissimilarity.

I'm using R and have explored several packages, but cannot find a function to generate a standard cosine dissimilarity matrix. The built-in dist() function doesn't support cosine distances, also within the package arules there is a dissimilarity() function, but it only works on binary data.

Can anybody recommend a library? Or demonstrated how to calculate cosine dissimilarity within R?

It may be faster to write your own cosine dissimilarity function. — assumednormal, Jul 03 '12 at 12:45
Cosine is similarity, not dissimilarity. You can, however, turn cosine into euclidean distance of scaled data: d=sqrt(2*(1-cos)). — ttnphns, Jul 03 '12 at 14:51
Same question over on SO: Find cosine similarity between two arrays — smci, Mar 30 '17 at 21:03

Macro · Accepted Answer · 2012-07-05T13:40:33.530

36

As @Max indicated in the comments (+1) it would be simpler to "write your own" than to spend time looking for it somewhere else. As we know, the cosine similarity between two vectors $A,B$ of length $n$ is

$$ C = \frac{ \sum \limits_{i=1}^{n}A_{i} B_{i} }{ \sqrt{\sum \limits_{i=1}^{n} A_{i}^2} \cdot \sqrt{\sum \limits_{i=1}^{n} B_{i}^2} } $$

which is straightforward to generate in R. Let X be the matrix where the rows are the values we want to compute the similarity between. Then we can compute the similarity matrix with the following R code:

cos.sim <- function(ix) 
{
    A = X[ix[1],]
    B = X[ix[2],]
    return( sum(A*B)/sqrt(sum(A^2)*sum(B^2)) )
}   
n <- nrow(X) 
cmb <- expand.grid(i=1:n, j=1:n) 
C <- matrix(apply(cmb,1,cos.sim),n,n)

Then the matrix C is the cosine similarity matrix and you can pass it to whatever heatmap function you like (the only one I'm familiar with is image()).

edited Jul 05 '12 at 13:40

answered Jul 03 '12 at 14:33

Macro

44,826

Thanks, this is helpful. Actually, I don't want to plot the matrix itself but rather have a distance function for clustering of another heatmap that I have. – Greg Slodkowicz Jul 05 '12 at 12:01
@GregSlodkowicz, OK well perhaps you can pass this matrix to the function you're using. Also, if you've found this answer helpful please consider an upvote (or accepting the answer if you consider it definitive) :) – Macro Jul 05 '12 at 12:26
Great, thanks to your reply and ttnphns's comment I was able to do what I want. Now I would like to have a different metric when clustering rows than when clustering columns but maybe that's pushing it... – Greg Slodkowicz Jul 07 '12 at 10:20
Apparently I don't have enough points to be able to comment. I just wanted to offer a slightly modified version of Macro's nice answer. Here it is. # ChirazB's version of cos.sim() by Macro
where S = X %*% t(X)

cos.sim.2 <- function(S,ix) { i <- ix[1] j <- ix[2] return( S[i,j]/sqrt(S[i,i]S[j,j]) ) } #test X <- matrix(rnorm(20),nrow=5,ncol=4) S <- X%%t(X) n <- nrow(X) idx.arr <- expand.grid(i=1:n, j=1:n) C <- matrix(apply(idx.arr,1,cos.sim,X),n,n) C2 <- matrix(apply(idx.arr,1,cos.sim.2,S),n,n) I don't like global variable, that's why I included S as a parameter.
– Chiraz BenAbdelkader Jan 11 '15 at 17:23
1

it should be sqrt(sum(A^2))*sqrt(sum(B^2)) instead of sqrt(sum(A^2)*sum(B^2)) – Marcin Aug 25 '21 at 09:02
Why? Does it make any difference? – WJH Jun 12 '23 at 12:47

Brad · Answer 2 · 2020-11-20T05:41:48.653

30

Many answers here are computationally inefficient, try this;

For cosine similarity matrix

Matrix <- as.matrix(DF)
sim <- Matrix / sqrt(rowSums(Matrix * Matrix))
sim <- sim %*% t(sim)

Convert to cosine dissimilarity matrix (distance matrix).

D_sim <- as.dist(1 - sim)

edited Nov 20 '20 at 05:41

answered Sep 17 '18 at 02:46

Brad

600

4

Awesome answer. At least 250x as fast as library(lsa) cosine() when using OpenBLAS and 96 cores. – webb Nov 13 '20 at 11:27
3

I'm glad you appreciate good computational mathematics. – Brad Jan 28 '21 at 12:41
3

Way faster than other functions. Thank you Brad. – patL May 04 '21 at 17:09

score 11 · Answer 3 · answered May 09 '14 at 12:53

11

You can use the cosine function from the lsa package:
http://cran.r-project.org/web/packages/lsa

answered May 09 '14 at 12:53

vonjd

6,146

3

Brad's answer is at least 250x as fast as library(lsa) cosine() when using OpenBLAS and 96 cores. – webb Nov 13 '20 at 11:27
@Downvoter: What is wrong with my answer??? – vonjd Aug 26 '21 at 08:40
1

I did not downvote your answer, so I don't know why it was downvoted. – webb Aug 26 '21 at 12:49

score 6 · Answer 4 · answered May 05 '15 at 14:24

The following function might be useful when working with matrices, instead of 1-d vectors:

# input: row matrices 'ma' and 'mb' (with compatible dimensions)
# output: cosine similarity matrix

cos.sim=function(ma, mb){
  mat=tcrossprod(ma, mb)
  t1=sqrt(apply(ma, 1, crossprod))
  t2=sqrt(apply(mb, 1, crossprod))
  mat / outer(t1,t2)
}

score 1 · Answer 5 · answered May 22 '18 at 20:43

Ramping up some of the previous code (from @Macro) on this issue, we can wrap this into a cleaner version in the following:

df <- data.frame(t(data.frame(c1=rnorm(100),
                              c2=rnorm(100),
                              c3=rnorm(100),
                              c4=rnorm(100),
                              c5=rnorm(100),
                              c6=rnorm(100))))

#df[df > 0] <- 1
#df[df <= 0] <- 0



apply_cosine_similarity <- function(df){
  cos.sim <- function(df, ix) 
  {
    A = df[ix[1],]
    B = df[ix[2],]
    return( sum(A*B)/sqrt(sum(A^2)*sum(B^2)) )
  }   
  n <- nrow(df) 
  cmb <- expand.grid(i=1:n, j=1:n) 
  C <- matrix(apply(cmb,1,function(cmb){ cos.sim(df, cmb) }),n,n)
  C
}
apply_cosine_similarity(df)

Hope this helps!

it should be sqrt(sum(A^2))sqrt(sum(B^2)) instead of sqrt(sum(A^2)sum(B^2)) — Marcin, Aug 25 '21 at 09:06

Compute a cosine dissimilarity matrix in R

5 Answers5

where S = X %*% t(X)

The following function might be useful when working with matrices, instead of 1-d vectors:

Linked