Taking Neural Network's false positives as the recommendation system result?
1) Is regression, not classification.

You should try to think of it from a decision tree perspective instead of NN. Your attributes for a customer are all products of this customer and all additional information about that customar.

Since the task is regression, all leafs of the decision tree will have the label 0 (if the decision path leads to the statement that the customer doesn't have the product) or the label 1 if the decision path leads to the statement that the customer has the product.

When building the decision tree, we start at the root where we have to decide which attribute we will use as the first node from where all the customers will take the corresponding branch depending on their value of the chosen attribute. This attribute is choosen by using entropy to calculate the attribute with the highest information-gain value. This simply means that we choose the attribute, that divides the customers into sets where each set has ideally the same amount of customers with 0 and 1.

This is repeated for each new node that branch from the parent node as long as there is an attribute left with information-gain above a threshold value or when the tree becomes to deep (since it is NP-complete).
Now we count at each leaf the amount of zeros and ones and label the leaf as max(0,1).
The conclusion of this: if a customer landed at a 1-leaf although he was 0 means, the highest information-gain attributes have the same values for this customer as they much more often do for customers who are 1.