On the Instability of Embeddings for Recommender Systems: the Case of Matrix Factorization

Most state-of-the-art top-N collaborative recommender systems work by learning embeddings to jointly represent users and items. Learned embeddings are considered to be effective to solve a variety of tasks. Among others, providing and explaining recommendations. In this paper we question the reliability of the embeddings learned by Matrix Factorization (MF). We empirically demonstrate that, by simply changing the initial values assigned to the latent factors, the same MF method generates very different embeddings of items and users, and we highlight that this effect is stronger for less popular items. To overcome these drawbacks, we present a generalization of MF, called Nearest Neighbors Matrix Factorization (NNMF). The new method propagates the information about items and users to their neighbors, speeding up the training procedure and extending the amount of information that supports recommendations and representations. We describe the NNMF variants of three common MF approaches, and with extensive experiments on five different datasets we show that they strongly mitigate the instability issues of the original MF versions and they improve the accuracy of recommendations on the long-tail.