  This paper contributes improvements on both the effectiveness and efficiency
of Matrix Factorization (MF) methods for implicit feedback. We highlight two
critical issues of existing works. First, due to the large space of unobserved
feedback, most existing works resort to assign a uniform weight to the missing
data to reduce computational complexity. However, such a uniform assumption is
invalid in real-world settings. Second, most methods are also designed in an
offline setting and fail to keep up with the dynamic nature of online data. We
address the above two issues in learning MF models from implicit feedback. We
first propose to weight the missing data based on item popularity, which is
more effective and flexible than the uniform-weight assumption. However, such a
non-uniform weighting poses efficiency challenge in learning the model. To
address this, we specifically design a new learning algorithm based on the
element-wise Alternating Least Squares (eALS) technique, for efficiently
optimizing a MF model with variably-weighted missing data. We exploit this
efficiency to then seamlessly devise an incremental update strategy that
instantly refreshes a MF model given new feedback. Through comprehensive
experiments on two public datasets in both offline and online protocols, we
show that our eALS method consistently outperforms state-of-the-art implicit MF
methods. Our implementation is available at
https://github.com/hexiangnan/sigir16-eals.
