As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph under investigation is directed or not. Thus, some important properties of undirected graph\textemdash symmetry on edges, for example\textemdash is ignored. In this paper, we propose a parallel PageRank algorithm specifically designed for undirected graphs that can fully leverage their symmetry. Formally, our algorithm extends the Chebyshev Polynomial approximation from the field of real function to the field of matrix function. Essentially, it reflects the symmetry on edges of undirected graph and the density of diagonalizable matrix. Theoretical analysis indicates that our algorithm has a higher convergence rate and requires less computation than the Power method, with the convergence rate being up to 50\% higher with a damping factor of $c=0.85$. Experiments on six datasets illustrate that our algorithm with 38 parallelism can be up to 39 times faster than the Power method.
翻译:根据图表结构,PageRank在多个领域广泛应用了顶点重要性的测量方法,PageRank在过去几十年中提出了许多PageRank算法,但其中很少考虑调查中的图表是否定向。因此,边缘非定向图形/textemdash对称性的某些重要属性被忽略,例如\ textemdash。在本文中,我们建议为非定向图形专门设计一个平行的PageRank算法,可以充分利用其对称性。形式上,我们的算法将Chebyshev多边近似法从实际功能领域扩大到矩阵功能领域。基本上,它反映了非定向图形边缘的对称性和可变矩阵的密度。理论分析表明,我们的算法的趋同率更高,需要比电力方法少的计算,而趋同率则提高到50<unk> 以上,而缩放系数为$c=0.85。在六个数据集上进行的实验表明,我们具有38个平行参数的算法可以比动力方法快39倍。</s>