基于迭代对角估计的线性复杂度SimRank计算
Linear complexity SimRank computation based on the iterative diagonal estimation
摘要：
本文提出了一种确定性线性时间复杂度IDE-SimRank方法来近似计算SimRank，并证明了其误差界。SimRank是一种著名的图顶点之间的相似性度量，它仅依赖于图拓扑，并且建立在“如果两个对象与相似对象相关，则它们相似”的直觉上。用于直接SimRank计算的不动点方程是在右侧具有特定对角矩阵的离散李雅普诺夫方程。该方法基于GMRES对该对角矩阵的估计，并使用该估计来计算单源和单对查询。这些计算的执行与系列收敛到离散李雅普诺夫方程解的一部分。
英文摘要：
This paper presents a deterministic linear time complexity IDE-SimRank method to approximately compute SimRank with proved error bound. SimRank is a well-known similarity measure between graph vertices which relies on graph topology only and is built on intuition that "two objects are similar if they are related to similar objects". The fixed point equation for direct SimRank computation is the discrete Lyapunov equation with specific diagonal matrix in the right hand side. The proposed method is based on estimation of this diagonal matrix with GMRES and use this estimation to compute singe-source and single pairs queries. These computations are executed with the part of series converging to the discrete Lyapunov equation solution.
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