Let's start with an example to exemplify how Apache SystemML works internally. Consider a recommender system.
A recommender system tries to predict the potential items that a user might be interested in, based on a history from other users.
So let's consider a so-called item-user or product-customer matrix, as illustrated here:
This is a so-called sparse matrix because only a couple of cells are populated with non-zero values indicating a match between a customer i and a product j. Either by just putting a one in the cell or any other numerical value, for example, indicating the number of products bought or a rating for that particular product j from customer i. Let's call this matrix rui, where u stands for user and i for item.
Those of you familiar with linear algebra might know that any matrix can be factorized by two smaller matrices. This means that you have to find two matrices pu and qi that,...