Before delving into true collaborative filtering, let's look at some baseline predictors that can predict ratings for new users who haven't rated anything yet, which makes it almost impossible to find out the neighborhood of such users. For such users, a basic baseline rating can be the average of all ratings. The problem with applying collaborative filtering in order to predict the ratings of items for new users is referred to as Cold Start in collaborative filtering literature.
The baseline predictor is normally denoted by 
for user 
and item 
. The base case where the baseline is set as equal to the global average of all ratings is given by the following formula:
However, this can be optimized using the average of that user's rating for other items (if any are available) or the average rating for that particular item (given by all other users). In these two cases, the baseline predictor is calculated using the following formulae:
Note that the subscript 
is used to denote...
