User based collaborative filtering issue

Question

In the user based Collaborative Filtering, the picture shows the formula of how to predict the rating of an item. And the NSa is the nearest neighbor set of user a. j is the item to be predicted. rij means the rating of item j by the user i in the NSa. So, my question is,what if the user i has never voted the item j? How to handle the rij? Thanks!

Answer 1

The sum is really over all the users in NSa that have also rated j. That's the usual answer, to restrict it this way too. You could also use some dummy value here when it doesn't exist, like using the average rating of user i instead. I don't recommend this as it slows things down without adding information.