Netflix prize tribute: Recommendation algorithm in Python

SVD doesn't work when you have a sparse matrix as input. You could use some sort of imputation method (like EM) to fill in all of the missing values then run SVD, but this would be extremely inefficient, since only a tiny fraction of the user x movies matrix of ratings is observed. It also probably wouldn't work very well, because your true signal from the data would be overwhelmed by all of the missing values that you'd somewhat arbitrarily filled in.

PMF is a generalization of SVD that is able to work directly on the sparse structure of the input. It does gradient descent -- modifying the low dimension latent vectors directly to minimize error, and never does any imputation of missing values. This makes it very efficient, and it can easily handle millions of ratings. See http://www.cs.toronto.edu/~amnih/papers/pmf.pdf for an application of PMF to the very large Netflix problem.