Interpretation of matrix factorization results

Matrix factorization methods are known to give good results pertaining to problems like movie recommendation. The method reduces the feature space, which is then used for recommendations.

For example consider user item matrix where each element is rating by a user for a product, whose dimension is (lets say) 1000 by 20000. We can apply matrix factorization to this matrix with latent feature size=10. This will result in user latent feature matrix P of size 1000 by 10, and item latent feature matrix Q of size 10 by 20000. Each row of P would represent the strength of the associations between a user and the features. Similarly, each row of Q would represent the strength of the associations between an item and the features.

How do we interpret this reduced latent feature space? What is the relation between reduced latent feature space and actual feature space?

• Hi, Can you explain your question more. people might not be familiar with some terms. Then asking a question without explaining the aspects or some example is difficult to be solved. Thanks. – TPArrow Jun 26 '15 at 8:24
• The latent space is simply the range of latent variables in the general statistical sense: en.wikipedia.org/wiki/Latent_variable. The latent features may or may not correspond to intuitve factors (like genre for movies). – sandris Jul 16 '15 at 8:30