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首页> 外文期刊>Journal of Statistical Physics >Bootstrapping on Undirected Binary Networks Via Statistical Mechanics
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Bootstrapping on Undirected Binary Networks Via Statistical Mechanics

机译：通过统计力学在无向二元网络上进行引导

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We propose a new method inspired from statistical mechanics for extracting geometric information from undirected binary networks and generating random networks that conform to this geometry. In this method an undirected binary network is perceived as a thermodynamic system with a collection of permuted adjacency matrices as its states. The task of extracting information from the network is then reformulated as a discrete combinatorial optimization problem of searching for its ground state. To solve this problem, we apply multiple ensembles of temperature regulated Markov chains to establish an ultrametric geometry on the network. This geometry is equipped with a tree hierarchy that captures the multiscale community structure of the network. We translate this geometry into a Parisi adjacency matrix, which has a relative low energy level and is in the vicinity of the ground state. The Parisi adjacency matrix is then further optimized by making block permutations subject to the ultrametric geometry. The optimal matrix corresponds to the macrostate of the original network. An ensemble of random networks is then generated such that each of these networks conforms to this macrostate; the corresponding algorithm also provides an estimate of the size of this ensemble. By repeating this procedure at different scales of the ultrametric geometry of the network, it is possible to compute its evolution entropy, i.e. to estimate the evolution of its complexity as we move from a coarse to a fine description of its geometric structure. We demonstrate the performance of this method on simulated as well as real data networks.
机译：我们提出了一种受统计力学启发的新方法，该方法可从无向二进制网络中提取几何信息，并生成符合该几何的随机网络。在这种方法中，无向二元网络被认为是一个热力学系统，具有一系列邻接矩阵作为其状态。从网络中提取信息的任务然后被重新构造为搜索其基态的离散组合优化问题。为了解决这个问题，我们应用了多个温度调节马尔可夫链的集成体，以在网络上建立超几何。这种几何结构配备了树状层次结构，可捕获网络的多尺度社区结构。我们将此几何图形转换为Parisi邻接矩阵，该矩阵具有相对较低的能级并且处于基态附近。然后，通过使块排列服从于超几何尺寸，进一步优化Parisi邻接矩阵。最佳矩阵对应于原始网络的宏观状态。然后，生成一组随机网络，以使这些网络中的每一个都符合该宏状态。相应的算法还提供了该集合大小的估计。通过在网络的超度量几何的不同尺度上重复此过程，可以计算其演化熵，即，随着我们从对其几何结构的粗略描述到精细描述的转变，估计其复杂性的演化。我们演示了该方法在模拟和实际数据网络上的性能。

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