基于凸优化的网络社团结构识别
Identification of community structure in networks with convex optimization
摘要：
我们将网络分区集上的模块度最大化问题转化为完全正锥上的锥优化问题，将其从组合优化问题转化为凸连续优化问题。一个半定松弛的圆锥形程序，然后允许计算上界的最大模块化的网络。基于相应的半定规划的解，我们设计了一个随机化算法，生成具有次优模块度的网络分区。我们将此算法应用于几个基准网络，证明它是竞争力的准确性与以前已知的最好的算法。我们使用我们的方法提供了第一个证明的最优性的分区为现实世界的网络。
英文摘要：
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous one. A semidefinite relaxation of this conic program then allows to compute upper bounds on the maximum modularity of the network. Based on the solution of the corresponding semidefinite program, we design a randomized algorithm generating partitions of the network with suboptimal modularities. We apply this algorithm to several benchmark networks, demonstrating that it is competitive in accuracy with the best algorithms previously known. We use our method to provide the first proof of optimality of a partition for a real-world network.
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。
