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像嵌入中平衡局部与全局结构（LGS）的方法。部分嵌入方法致力于捕捉全局结构，而另一些方法则试图保留局部邻域关系。同时兼顾两者的方法较为罕见，且在二维空间中（大多数图绘制领域的工作场景）完美保留局部与全局信息往往难以实现。可视化任务中选择局部或全局嵌入不仅取决于任务需求，还取决于底层数据的结构特性——而这一特性可能无法预先获知。针对给定图结构，LGS旨在寻找保留局部与全局结构的最优平衡点。我们通过合成数据集与真实数据集验证了LGS的性能，结果表明其在压力（stress）及邻域保留等既有质量指标上具有与最先进方法竞争的实力。为评估中间结构捕获能力，我们引入了一种新的质量度量——簇距离保留度。所有源代码、数据集、实验与分析结果均已在线公开。