  A key challenge of the collaborative filtering (CF) information filtering is
how to obtain the reliable and accurate results with the help of peers'
recommendation. Since the similarities from small-degree users to large-degree
users would be larger than the ones opposite direction, the large-degree users'
selections are recommended extensively by the traditional second-order CF
algorithms. By considering the users' similarity direction and the second-order
correlations to depress the influence of mainstream preferences, we present the
directed second-order CF (HDCF) algorithm specifically to address the challenge
of accuracy and diversity of the CF algorithm. The numerical results for two
benchmark data sets, MovieLens and Netflix, show that the accuracy of the new
algorithm outperforms the state-of-the-art CF algorithms. Comparing with the CF
algorithm based on random-walks proposed in the Ref.7, the average ranking
score could reach 0.0767 and 0.0402, which is enhanced by 27.3\% and 19.1\% for
MovieLens and Netflix respectively. In addition, the diversity, precision and
recall are also enhanced greatly. Without relying on any context-specific
information, tuning the similarity direction of CF algorithms could obtain
accurate and diverse recommendations. This work suggests that the user
similarity direction is an important factor to improve the personalized
recommendation performance.
