Database Reference
In-Depth Information
A simple movie-rating matrix
Matrix factorization (or matrix completion) attempts to directly model this user-item mat-
rix by representing it as a product of two smaller matrices of lower dimension. Thus, it is
a dimensionality-reduction technique. If we have
U
users and
I
items, then our user-item
matrix is of dimension U x I and might look something like the one shown in the follow-
ing diagram:
A sparse ratings matrix
If we want to find a lower dimension (low-rank) approximation to our user-item matrix
with the dimension
k
, we would end up with two matrices: one for users of size U x k and
one for items of size I x k. These are known as factor matrices. If we multiply these two
factor matrices, we would reconstruct an approximate version of the original ratings mat-
rix. Note that while the original ratings matrix is typically very sparse, each factor matrix
is dense, as shown in the following diagram:
