We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underlying data, which may not be known in advance. For a given graph, LGS aims to find a good balance between the local and global structure to preserve. We evaluate the performance of LGS with synthetic and real-world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online.

翻译：我们提出了一种通过可调参数在图嵌入中平衡局部与全局结构（LGS）的方法。部分嵌入方法侧重于捕获全局结构，而另一些方法则致力于保持局部邻域关系。鲜有方法尝试同时兼顾两者，且在高维数据可视化中常需降维至二维时，往往难以完美保留局部与全局信息。选择使用局部或全局嵌入进行可视化不仅取决于具体任务，还受制于基础数据的结构特征——而后者可能事先未知。针对给定图结构，LGS旨在寻找局部与全局结构之间的最优平衡点。我们通过合成数据集与真实数据集对LGS性能进行评估，结果表明：在应力（stress）与邻域保持（neighborhood preservation）等既定质量标准上，该方法与现有最优方法具有竞争力。我们引入了一种新的质量度量——聚类距离保持（cluster distance preservation），用于评估中间结构的捕获效果。所有源代码、数据集、实验过程及分析结果均已在线公开。