I have a matrix which I want to convert to one with binary output (0 vs 1). The matrix to be converted contains four rows of rankings (1 to 4):
mat1.data <- c(4, 3, 3, 3, 3, 2, 2, 1, 1, 1,
3, 4, 2, 4, 2, 3, 1, 3, 3, 2,
2, 2, 4, 1, 1, 1, 4, 4, 2, 4,
1, 1, 1, 2, 4, 4, 3, 2, 4, 3)
mat1 <- matrix(mat1.data,nrow=4,ncol=10,byrow=TRUE)
mat1
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 4 3 3 3 3 2 2 1 1 1
[2,] 3 4 2 4 2 3 1 3 3 2
[3,] 2 2 4 1 1 1 4 4 2 4
[4,] 1 1 1 2 4 4 3 2 4 3
For each row in the input matrix, I want to create four binary rows - one row for each value of the ranks (1-4). In the binary matrix, each row-wise entry is 1 on positions where the focal rank occurs in the input matrix, and 0 otherwise. Each row from the original matrix should produce 10*4=40 entries in the output matrix.
For example, for the first row of in the input matrix...
4 3 3 3 3 2 2 1 1 1
...the output should be:
0 0 0 0 0 0 0 1 1 1 # Rank 1 in input
0 0 0 0 0 1 1 0 0 0 # Rank 2 in input
0 1 1 1 1 0 0 0 0 0 # Rank 3 in input
1 0 0 0 0 0 0 0 0 0 # Rank 4 in input
Continue with this process, the expected output for all four rows of rankings should look like this:
0 0 0 0 0 0 0 1 1 1 #first row of rankings starts
0 0 0 0 0 1 1 0 0 0
0 1 1 1 1 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 #first row of rankings ends
0 0 0 0 0 0 1 0 0 0 #second row of rankings starts
0 0 1 0 1 0 0 0 0 1
1 0 0 0 0 1 0 1 1 0
0 1 0 1 0 0 0 0 0 0 #second row of rankings ends
0 0 0 1 1 1 0 0 0 0 #third row of rankings starts
1 1 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 1 0 1 #third row of rankings ends
1 1 1 0 0 0 0 0 0 0 #fourth row of rankings starts
0 0 0 1 0 0 0 1 0 0
0 0 0 0 0 0 1 0 0 1
0 0 0 0 1 1 0 0 1 0 #fourth row of rankings ends
How do I do achieve this? I have a larger dataset and so a more efficient method is preferred but any help will be greatly appreciated!
matrix(sapply(mat1, \(i) replace(numeric(4), i, 1)), ncol = ncol(mat1))
# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,] 0 0 0 0 0 0 0 1 1 1
# [2,] 0 0 0 0 0 1 1 0 0 0
# [3,] 0 1 1 1 1 0 0 0 0 0
# [4,] 1 0 0 0 0 0 0 0 0 0
# [5,] 0 0 0 0 0 0 1 0 0 0
# [6,] 0 0 1 0 1 0 0 0 0 1
# [7,] 1 0 0 0 0 1 0 1 1 0
# [8,] 0 1 0 1 0 0 0 0 0 0
# [9,] 0 0 0 1 1 1 0 0 0 0
#[10,] 1 1 0 0 0 0 0 0 1 0
#[11,] 0 0 0 0 0 0 0 0 0 0
#[12,] 0 0 1 0 0 0 1 1 0 1
#[13,] 1 1 1 0 0 0 0 0 0 0
#[14,] 0 0 0 1 0 0 0 1 0 0
#[15,] 0 0 0 0 0 0 1 0 0 1
#[16,] 0 0 0 0 1 1 0 0 1 0
It takes 2 steps, and piping syntax may look clearer:
sapply(mat1, \(i) replace(numeric(4), i, 1)) |> ## each value to binary vector
matrix(ncol = ncol(mat1)) ## reshape
Actually, I don't need that anonymous function \(i). I can pass replace, and its arguments, to sapply directly.
matrix(sapply(mat1, replace, x = numeric(4), values = 1), ncol = ncol(mat1))
sapply(mat1, replace, x = numeric(4), values = 1) |> matrix(ncol = ncol(mat1))
Misc
user20650 and I discussed a little bit in comments, and here is a "vectorized" approach using outer:
matrix(+outer(1:4, c(mat1), "=="), ncol = ncol(mat1))
Henrik's answer is a more memory-efficient "vectorized" approach, but it over-complicates the index computation. Here is something simpler:
out <- matrix(0, nrow(mat1) * 4, ncol(mat1))
pos1 <- seq(0, length(mat1) - 1) * 4 + c(mat1)
out[pos1] <- 1
All methods so far create a dense output matrix. This is OK because the percentage of nonzero elements is 25%, which is not typically sparse. However, in case we want a sparse one, it is also straightforward:
## in fact, this is what Henrik aims to compute
ij <- arrayInd(pos1, c(4 * nrow(mat1), ncol(mat1)))
## sparse matrix
Matrix::sparseMatrix(i = ij[, 1], j = ij[, 2], x = rep(1, length(mat1)))
#16 x 10 sparse Matrix of class "dgCMatrix"
#
# [1,] . . . . . . . 1 1 1
# [2,] . . . . . 1 1 . . .
# [3,] . 1 1 1 1 . . . . .
# [4,] 1 . . . . . . . . .
# [5,] . . . . . . 1 . . .
# [6,] . . 1 . 1 . . . . 1
# [7,] 1 . . . . 1 . 1 1 .
# [8,] . 1 . 1 . . . . . .
# [9,] . . . 1 1 1 . . . .
#[10,] 1 1 . . . . . . 1 .
#[11,] . . . . . . . . . .
#[12,] . . 1 . . . 1 1 . 1
#[13,] 1 1 1 . . . . . . .
#[14,] . . . 1 . . . 1 . .
#[15,] . . . . . . 1 . . 1
#[16,] . . . . 1 1 . . 1 .