Calculating the row wise cosine similarity using matrix multiplication in R

Question

In the below example I have calculated the row wise cosine similarity for data in a matrix using a custom function and a for loop. The output that I would like is a symmetric matrix.

I would like to implement this calculation using matrix multiplication (linear algebra) without a for loop as the actual input matrix I need to work on is much larger and a loop will be too slow.

x = c(0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1)
x = matrix(x, nrow = 3, byrow = TRUE)

cosine_similarity = function(a, b){
  y = crossprod(a, b) / sqrt(crossprod(a) * crossprod(b))
  return(y)
}

N_row = dim(x)[1]

similarity_matrix = matrix(0, nrow = N_row, ncol = N_row)

for (i in 1:(N_row-1)) {
  for (j in (i + 1):N_row) {
    similarity_matrix[i,j] = cosine_similarity(x[i,], x[j,])
  }
}

similarity_matrix = similarity_matrix + t(similarity_matrix)

Answer 1

We could use outer to make this faster

outer(seq_len(nrow(x)), seq_len(nrow(x)), 
    FUN = Vectorize(function(i, j) cosine_similarity(x[i,], x[j, ])))

-output

#          [,1]      [,2]      [,3]
#[1,] 1.0000000 0.5000000 0.4082483
#[2,] 0.5000000 1.0000000 0.4082483
#[3,] 0.4082483 0.4082483 1.0000000

---

or another option is combn

out <- diag(nrow(x)) * 0
out[upper.tri(out)] <-  combn(seq_len(nrow(x)), 2,
     FUN = function(i) c(cosine_similarity(x[i[1], ], x[i[2],])))
out <- out + t(out)
diag(out) <- 1