  The dynamic environment in the real world calls for the adaptive techniques
for information filtering, namely to provide real-time responses to the changes
of system data. Where many incremental algorithms are designed for this
purpose, they are usually challenged by the worse and worse performance
resulted from the cumulative errors over time. In this Letter, we propose two
incremental diffusion-based algorithms for the personalized recommendations,
which integrate some pieces of local and fast updatings to achieve the
approximate results. In addition to the fast responses, the errors of the
proposed algorithms do not cumulate over time, that is to say, the global
recomputing is unnecessary. This remarkable advantage is demonstrated by
several metrics on algorithmic accuracy for two movie recommender systems and a
social bookmarking system.
