Giora Simchoni - 6 months ago 47

R Question

I have two sparse matrices A and B (

`slam::simple_triplet_matrix`

I wish to calculate the cosine distance between each pair of rows (i.e. row 1 from matrix A and row 1 from matrix B, row 2 from matrix A and row 2 from matrix B, etc.).

I can do this using a for-loop or using

`apply`

`library(slam)`

A <- simple_triplet_matrix(1:3, 1:3, 1:3)

B <- simple_triplet_matrix(1:3, 3:1, 1:3)

cosine <- NULL

for (i in 1:(dim(A)[1])) {

a <- as.vector(A[i,])

b <- as.vector(B[i, ])

cosine[i] <- a %*% b / sqrt(a%*%a * b%*%b)

}

I understand something in this previously asked question might help me, but:

a) This isn't really what I want, I just want M cosine distances for M rows, not all pairwise correlations between rows of a given sparse matrix.

b) I admit to not fully understanding the math behind this 'vectorized' solution so maybe some explanation would come in handy.

Thank you.

EDIT: This is also NOT a duplicate of this question as I'm not just interested in a regular cosine computation on two simple vectors (I clearly know how to do this, see above), I'm interested in a much larger scale situation, specifically involving slam sparse matrices.

Answer

According to the documentation, element-by-element (array) multiplication of compatible `simple_triplet_matrices`

and `row_sums`

of `simple_triplet_matrices`

are available. With these operators/functions, the computation is:

```
cosineDist <- function(A, B){
row_sums(A * B) / sqrt(row_sums(A * A) * row_sums(B * B))
}
```

Notes:

`row_sums(A * B)`

computes the dot product of each row in`A`

and its corresponding row in`B`

, which is the numerator term in your`cosine`

. The result is a vector (not sparse) whose elements are these dot products for each corresponding row in A and B.`row_sums(A * A)`

computes the squared 2-norm of each row in`A`

. The result is a vector (not sparse) whose elements are these squared 2-norms for each row in A.- Similarly,
`row_sums(B * B)`

computes the squared 2-norm of each row in`B`

. The result is a vector (not sparse) whose elements are these squared 2-norms for each row in B. - The rest of the computation operates on these vectors whose elements are for each row of A and/or B.