In this paper, based on a weighted projection of bipartite user-object network, we introduce a personalized recommendation algorithm, called the emph{network-based inference} (NBI), which has higher accuracy than the classical algorithm, namely emph{collaborative filtering}. In the NBI, the correlation resulting from a specific attribute may be repeatedly counted in the cumulative recommendations from different objects. By considering the higher order correlations, we design an improved algorithm that can, to some extent, eliminate the redundant correlations. We test our algorithm on two benchmark data sets, emph{MovieLens} and emph{Netflix}. Compared with the NBI, the algorithmic accuracy, measured by the ranking score, can be further improved by 23% for emph{MovieLens} and 22% for emph{Netflix}, respectively. The present algorithm can even outperform the emph{Latent Dirichlet Allocation} algorithm, which requires much longer computational time. Furthermore, most of the previous studies considered the algorithmic accuracy only, in this paper, we argue that the diversity and popularity, as two significant criteria of algorithmic performance, should also be taken into account. With more or less the same accuracy, an algorithm giving higher diversity and lower popularity is more favorable. Numerical results show that the present algorithm can outperform the standard one simultaneously in all five adopted metrics: lower ranking score and higher precision for accuracy, larger Hamming distance and lower intra-similarity for diversity, as well as smaller average degree for popularity.
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