稀疏网络模块检测中的相变
Phase transition in the detection of modules in sparse networks
摘要：
我们提出了一个渐近精确的分析稀疏随机网络中的社区检测问题。我们的研究结果也适用于检测的功能模块，分区和着色在嘈杂的种植模型。使用腔的方法分析，我们揭示了一个相变从一个区域，其中原来的组分配是不可检测的检测是可能的。在某些情况下，可检测区域分为算法上困难的区域和容易的区域。我们的方法自然转化为一个实用的算法，用于检测稀疏网络中的模块，并学习底层模型的参数。
英文摘要：
We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks. Our results are also applicable to detection of functional modules, partitions, and colorings in noisy planted models. Using a cavity method analysis, we unveil a phase transition from a region where the original group assignment is undetectable to one where detection is possible. In some cases, the detectable region splits into an algorithmically hard region and an easy one. Our approach naturally translates into a practical algorithm for detecting modules in sparse networks, and learning the parameters of the underlying model.
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