大规模图的熵谱学习
Entropic Spectral Learning for Large-Scale Graphs
摘要：
图谱已被成功地用于分类网络类型，计算图之间的相似性，并确定网络中的社区数量。对于大型图，其中特征分解是不可行的，通常使用迭代矩匹配近似的频谱和核平滑。我们发现，基本的时刻信息丢失时，使用核平滑。我们进一步提出了一种基于最大熵方法的谱密度近似，并给出了一种新的算法。这种方法精确地匹配矩，并且处处为正。我们通过在合成网络（如Erdens-Rényi和Barabási-Albert随机图）和真实网络（如来自SNAP数据集的Orkut、YouTube和Amazon的社交网络）上的实验，证明了它在学习图谱方面优于现有方法的有效性和优越性。
英文摘要：
Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment matched approximations to the spectra and kernel smoothing are typically used. We show that the underlying moment information is lost when using kernel smoothing. We further propose a spectral density approximation based on the method of Maximum Entropy, for which we develop a new algorithm. This method matches moments exactly and is everywhere positive. We demonstrate its effectiveness and superiority over existing approaches in learning graph spectra, via experiments on both synthetic networks, such as the Erdős-Rényi and Barabási-Albert random graphs, and real-world networks, such as the social networks for Orkut, YouTube, and Amazon from the SNAP dataset.
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