PageRank和秩反转对阻尼因子的依赖性
PageRank and rank-reversal dependence on the damping factor
摘要：
PageRank（PR）是Google最初开发的一种算法，用于评估网页的重要性。考虑到Google的PR算法对于收集相关信息或现代企业的成功有多么根深蒂固，排名稳定性和阻尼因子（算法中的一个参数）的选择问题显然很重要。我们调查PR作为一个函数的阻尼因子d从万维网的一个域获得的网络上，发现排名反转经常发生在广泛的PR（和d）。我们使用三种不同的相关性度量，Pearson，Spearman和Kendall，来研究d变化时的秩反转，并表明PR向量的相关性随着d从其经常引用的值$d_0=0.85$的变化而迅速下降。秩反转也观察到通过测量斯皮尔曼和肯德尔秩相关，评估相对排名，而不是绝对PR。秩反转不仅发生在有向网络包含秩汇，但也在一个单一的强连接组件，根据定义不包含任何汇。我们将秩反转与有向网络结构中的秩口袋和瓶颈联系起来。对于所研究的网络，相对秩是更稳定的$d=0.65$比在$d=d_0$我们的措施。
英文摘要：
PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the question of rank-stability and choice of the damping factor (a parameter in the algorithm) is clearly important. We investigate PR as a function of the damping factor d on a network obtained from a domain of the World Wide Web, finding that rank-reversal happens frequently over a broad range of PR (and of d). We use three different correlation measures, Pearson, Spearman, and Kendall, to study rank-reversal as d changes, and show that the correlation of PR vectors drops rapidly as d changes from its frequently cited value, $d_0=0.85$. Rank-reversal is also observed by measuring the Spearman and Kendall rank correlation, which evaluate relative ranks rather than absolute PR. Rank-reversal happens not only in directed networks containing rank-sinks but also in a single strongly connected component, which by definition does not contain any sinks. We relate rank-reversals to rank-pockets and bottlenecks in the directed network structure. For the network studied, the relative rank is more stable by our measures around $d=0.65$ than at $d=d_0$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
