Experiments

Collaborative filtering is the task of predicting preferences (or producing personal recommendations) by using other people's preferences. The Netflix problem [14] is such a task. It consists of movie ratings given by $n=480189$ customers to $d=17770$ movies. There are $N=100480507$ ratings from 1 to 5 given, from which 1408395 ratings are reserved for validation (or probing). Note that 98.8% of the values are thus missing. We tried to find $c=15$ principal components from the data using a number of methods. We subtracted the mean rating for each movie, assuming 22 extra ratings of 3 for each movie as a Dirichlet prior.