Faster matrix multiplication by replacing a double loop

Question

I have a dataframe which looks a bit as produced by the following code (but much larger)

set.seed(10)    
mat <- matrix(rbinom(200, size=1, prob = .5), ncol = 10)

In the columns are issues and 1 indicates that an observation is interested in a specific issue. I want to generate a network comparing all observations and have a count of issues that each dyad is jointly interested in.

I have produced the following code, which seems to be working fine:

mat2 <- matrix(NA,20,20)

for(i in 1:nrow(mat)){
    for(j in 1:nrow(mat)){
       mat2[i,j] <- sum(as.numeric(mat[i,]==1) + as.numeric(mat[j,]==1) == 2)
    }
 }

So I compare every entry with every other entry, and only if both have a 1 entry (i.e., they are interested), then this sums to 2 and will be counted as joint interest in a topic.

My problem is that my dataset is very large, and the loop now runs for hours already.

Does anyone have an idea how to do this while avoiding the loop?

Answer 1

going ahead and promoting @jogo's comment as it is by far the fastest (thank's for the hint, I will use that in production as well).

set.seed(10)    
mat <- matrix(rbinom(200, size=1, prob = .5), ncol = 10)
mat2 <- matrix(NA,20,20)
binary_mat <- mat == 1
tmat <- t(mat==1)

microbenchmark::microbenchmark(
  "loop" = for(i in 1:nrow(mat)){
             for(j in 1:nrow(mat)){
               mat2[i,j] <- sum(as.numeric(mat[i,]==1) + as.numeric(mat[j,]==1) == 2)
             }
           }, 
  "apply" = mat4 <- apply(tmat, 2, function(x) colSums(tmat & x)), 
  "matrix multiplication" = mat5 <- mat %*% t(mat),
  "tcrossprod" = tcrossprod(mat),
  "tcrossprod binary" = tcrossprod(binary_mat)
)

On my machine this benchmark results in

Unit: microseconds
                  expr       min        lq        mean    median         uq       max neval cld
                  loop 16699.634 16972.271 17931.82535 17180.397 17546.1545 31502.706   100   b
                 apply   322.942   330.046   395.69045   357.886   368.8300  4299.228   100  a 
 matrix multiplication    21.889    28.801    36.76869    39.360    43.9685    50.689   100  a 
            tcrossprod     7.297     8.449    11.20218     9.984    14.4005    18.433   100  a 
     tcrossprod binary     7.680     8.833    11.08316     9.601    12.0970    35.713   100  a 

Answer 2

This should be faster:

tmat <- t(mat==1)
mat4 <- apply(tmat, 2, function(x) colSums(tmat & x))