ALTERNATING AUTOENCODERS FOR MATRIX COMPLETION

摘要

We consider autoencoders (AEs) for matrix completion (MC) with application to collaborative filtering (CF) for recommedation systems. It is observed that for a given sparse user-item rating matrix, denoted as ${oldsymbol {M}}$, an AE performs matrix factorization so that the recovered matrix is represented as a product of user and item feature matrices. Such an AE sequentially estimates user and item feature matrices: for the item-based AE (I-AE) that uses columns of M as its input vectors, the AE's encoder first estimates an item feature matrix and then the decoder estimates a user feature matrix based on the output of the encoder. Similarly, the user-based AE (U-AE) that uses the columns of ${oldsymbol {M}} ^{T, }$ as its input vectors first estimates a user feature matrix and then an item feature matrix. This sequential estimation can degrade the performance of the MC/CF, because the decoder depends on the output of the encoder. To enhance MC/CF performance, we propose alternating AEs (AAEs), a parallel algorithm employing both I-AE and U-AE and alternatively use them. We apply the AAE to synthetic, MovieLens 100k and 1M data sets. The results demonstrate that AAE can outperform all existing MC/CF methods.