Embedding nodes of a large network into a metric (e.g., Euclidean) space has become an area of active research in statistical machine learning, which has found applications in natural and social sciences. Generally, a representation of a network object is learned in a Euclidean geometry and is then used for subsequent tasks regarding the nodes and/or edges of the network, such as community detection, node classification and link prediction. Network embedding algorithms have been proposed in multiple disciplines, often with domain‐specific notations and details. In addition, different measures and tools have been adopted to evaluate and compare the methods proposed under different settings, often dependent of the downstream tasks. As a result, it is challenging to study these algorithms in the literature systematically. Motivated by the recently proposed PCS framework for Veridical Data Science, we propose a framework for network embedding algorithms and discuss how the principles of predictability, computability, and stability (PCS) apply in this context. The utilization of this framework in network embedding holds the potential to motivate and point to new directions for future research.

中文翻译：

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垂直网络嵌入的下一波浪潮*

将大型网络的节点嵌入度量（例如，欧几里得）空间已成为统计机器学习中积极研究的领域，该领域已在自然科学和社会科学中得到应用。通常，以欧几里得几何学学习网络对象的表示，然后将其用于有关网络的节点和/或边缘的后续任务，例如社区检测，节点分类和链接预测。网络嵌入算法已在多个学科中提出，通常带有特定于域的符号和详细信息。此外，已采用不同的措施和工具来评估和比较在不同设置下提出的方法，这些方法通常取决于下游任务。结果，在文献中系统地研究这些算法是具有挑战性的。可预测性，可计算性和稳定性（PCS）在此情况下适用。在网络嵌入中使用此框架具有激发和指出未来研究新方向的潜力。