A cost-based optimizer for machine learning algorithms

Let's start with an example to exemplify how Apache SystemML works internally. Consider a recommender system.

An example - alternating least squares

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 r_ui, 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 p_u and q_i that,...