Partitioning networks into clusters and residuals with average association.
Partitioning networks into clusters and residuals with average association.
复制标题
将网络划分为具有平均关联的簇和残差。
作者：
M. Vejmelka;M. Paluš
我们研究了在相互作用的系统网络中检测表现出高于平均水平的内部连通性的集群的问题。我们展示了在谱图聚类的上下文中形成的平均关联目标如何自然地导致聚类策略，其中每个系统被分配到至多一个聚类。剩余集由不是任何集群成员的系统形成。平均关联目标的最大化导致了一个难以解决的离散优化问题，但松弛的版本可以使用连通性矩阵的特征分解来求解。描述了一种从松弛解中提取聚类的简单方法，并通过将方差最大化解应用于松弛解来开发该方法，这导致了一种具有更高精度和灵敏度的方法。对理论连接性模型和耦合Lorenz振子晶格中的同步团簇进行了数值研究，表明了该方法的有效性。将该方法应用于实验获得的人体静息状态功能磁共振成像数据集，并对结果进行了讨论。
We investigate the problem of detecting clusters exhibiting higher-than-average internal connectivity in networks of interacting systems. We show how the average association objective formulated in the context of spectral graph clustering leads naturally to a clustering strategy where each system is assigned to at most one cluster. A residual set is formed of the systems that are not members of any cluster. Maximization of the average association objective leads to a discrete optimization problem, which is difficult to solve, but a relaxed version can be solved using an eigendecomposition of the connectivity matrix. A simple approach to extracting clusters from a relaxed solution is described and developed by applying a variance maximizing solution to the relaxed solution, which leads to a method with increased accuracy and sensitivity. Numerical studies of theoretical connectivity models and of synchronization clusters in a lattice of coupled Lorenz oscillators are conducted to show the efficiency of the proposed approach. The method is applied to an experimentally obtained human resting state functional magnetic resonance imaging dataset and the results are discussed.
DOI：
10.1073/pnas.0504136102
发表时间：
2005-07-05
影响因子：
11.1
作者：
Fox, MD;Snyder, AZ;Raichle, ME
通讯作者：
Raichle, ME