The element X[i, j]
on the i
-th row and j
-th column is represented
as a triple (i, j, X[i,k])
. The input for CMF is then a matrix
where each row specifies one element, and hence the representation
is of size N x 3
, where N
is the total number of observed entries.
In the original input matrix the missing entries should be marked
as NA
. In the output they will be completely omitted.
Even though this format reminds the representation often used
for representing sparse matrices, it is important to notice that
observed zeroes are retained in the representation. The
elements missing from this representation are considered unknown,
not zero.