  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 Veridical Data Science (VDS) framework, we
propose a framework for network embedding algorithms and discuss how the
principles of predictability, computability and stability 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.
