Knowledge Discovery in a Recommender System: The Matrix Factorization Approach

Two famous matrix factorization techniques, the Singular Value Decomposition (SVD) and the Nonnegative Matrix Factorization (NMF), are popularly used by recommender system applications. Recommender system data matrices have many missing entries, and to make them suitable for factorization, the missing entries need to be filled. For matrix completion, we use mean, median and mode as three different cases of imputation. The natural clusters produced after factorization are used to formulate simple out-of-sample extension algorithms and methods to generate recommendation for a new user. Two cluster evaluation measures, Normalized Mutual Information (NMI) and Purity are used to evaluate the quality of clusters.