This is a bit old and there is likely more complex systems. You can use a collaborative filtering algorithm, we can have one matrix where all columns are our users each row contains their ratings for the movies. Then we have another matrix where each column contains a feature for those movies, e.g. romance, action, drama... Our optimization algorithm would be; based on the current ratings from the users predict how would a newly joined user rate all of our movies, while simultaneously update the features for the movies.