复杂网络合并双曲嵌入的优化
Optimisation of the coalescent hyperbolic embedding of complex networks
摘要：
一些观察表明，在真实网络背后存在一个潜在的双曲空间，这使得它们的结构非常直观，因为连接的概率随着节点之间的双曲距离而减小。沿着这条线生成随机图的显着网络模型是流行度相似性优化（PSO）模型，同时提供无标度分布，高聚类和小世界属性。这些结果为双曲线嵌入算法的发展提供了强大的动力，该算法解决了基于网络结构的节点最佳双曲线坐标的问题。非中心最小曲线嵌入（ncMCE）方法是一种非常有前途的双曲线嵌入方法，属于合并嵌入算法家族。这种方法以较低的运行时间提供了高质量的嵌入。在目前的工作中，我们提出了一个进一步优化的角度坐标在这个框架中，似乎减少对数损失和增加贪婪的路由得分的嵌入相比，原始版本，从而增加了额外的改进推断的双曲线坐标的质量。
英文摘要：
Several observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network structure. A very promising recent approach for hyperbolic embedding is provided by the noncentered minimum curvilinear embedding (ncMCE) method, belonging to the family of coalescent embedding algorithms. This approach offers a high quality embedding at a low running time. In the present work we propose a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.
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