双曲空间中网络嵌入和链接预测的相似最小曲线自动机
Minimum curvilinear automata with similarity attachment for network embedding and link prediction in the hyperbolic space
摘要：
最小曲线线性（MC）的思想是复杂网络的隐藏几何，特别是当它们足够稀疏，聚类，小世界和异构时，可以使用最小生成树（MST）有效地导航，这是一个贪婪的导航器。局部拓扑信息驱动全局几何导航，MST可以被解释为一条增长路径，该路径通过全局最小化网络中节点的整体距离来最大化每一步所连接节点之间的局部相似性。这在没有网络结构和仅存在几何上位于高维空间中的网络生成流形上的节点时也是有效的。我们知道，双曲空间中的随机几何图是现实复杂网络的一个适当模型：对这种联系的解释是，复杂网络表现出分层的树状组织，而双曲几何又是树的几何。在这里，我们表明，根据一种机制，我们定义的相似性附件，访问节点序列的网络自动机可以有效地近似节点的角坐标在双曲盘，实际上代表了他们的相似性排序。这是MST在其贪婪增长过程中，在每一步都顺序地将最相似（较不遥远）的节点附加到其自己的队列的事实的结果。最小曲线自动机（MCA）的嵌入精度似乎优于HyperMap-CN，但不如合并嵌入，但其在真实网络上的链接预测性能是基于双曲空间的方法所没有的。最后，根据用于构建MST的数据结构，MCA的时间复杂度也可以接近于与边的数量的线性依赖。
英文摘要：
The idea of minimum curvilinearity (MC) is that the hidden geometry of complex networks, in particular when they are sufficiently sparse, clustered, small-world and heterogeneous, can be efficiently navigated using the minimum spanning tree (MST), which is a greedy navigator. The local topological information drives the global geometrical navigation and the MST can be interpreted as a growing path that greedily maximizes local similarity between the nodes attached at each step by globally minimizing their overall distances in the network. This is also valid in absence of the network structure and in presence of only the nodes geometrically located over the network generative manifold in a high-dimensional space. We know that random geometric graphs in the hyperbolic space are an adequate model for realistic complex networks: the explanation of this connection is that complex networks exhibit hierarchical, tree-like organization, and in turn the hyperbolic geometry is the geometry of trees. Here we show that, according to a mechanism that we define similarity attachment, the visited node sequence of a network automaton can efficiently approximate the nodes' angular coordinates in the hyperbolic disk, that actually represent an ordering of their similarities. This is a consequence of the fact that the MST, during its greedy growing process, at each step sequentially attaches the node most similar (less distant) to its own cohort. Minimum curvilinear automata (MCA) displays embedding accuracy which seems superior to HyperMap-CN and inferior to coalescent embedding, however its link prediction performance on real networks is without precedent for methods based on the hyperbolic space. Finally, depending on the data structure used to build the MST, the MCA's time complexity can also approach a linear dependence from the number of edges.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
