  The matrix factorization (MF) technique has been widely adopted for solving
the rating prediction problem in recommender systems. The MF technique utilizes
the latent factor model to obtain static user preferences (user latent vectors)
and item characteristics (item latent vectors) based on historical rating data.
However, in the real world user preferences are not static but full of
dynamics. Though there are several previous works that addressed this time
varying issue of user preferences, it seems (to the best of our knowledge) that
none of them is specifically designed for tracking concept drift in individual
user preferences. Motivated by this, we develop a Temporal Matrix Factorization
approach (TMF) for tracking concept drift in each individual user latent
vector. There are two key innovative steps in our approach: (i) we develop a
modified stochastic gradient descent method to learn an individual user latent
vector at each time step, and (ii) by the Lasso regression we learn a linear
model for the transition of the individual user latent vectors. We test our
method on a synthetic dataset and several real datasets. In comparison with the
original MF, our experimental results show that our temporal method is able to
achieve lower root mean square errors (RMSE) for both the synthetic and real
datasets. One interesting finding is that the performance gain in RMSE is
mostly from those users who indeed have concept drift in their user latent
vectors at the time of prediction. In particular, for the synthetic dataset and
the Ciao dataset, there are quite a few users with that property and the
performance gains for these two datasets are roughly 20% and 5%, respectively.
