Ultra accurate collaborative information filtering via directed user similarity

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.Comment: 6 pages, 4 figure

On the connectedness of planar self-affine sets

In this paper, we consider the connectedness of planar self-affine set $T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with characteristic polynomial $f(x)=x^2+bx+c$ and a digit set $\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected. Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively collinear.Comment: 18 pages; 18 figure