  Directed graphs are a natural model for many phenomena, in particular
scientific knowledge graphs such as molecular interaction or chemical reaction
networks that define cellular signaling relationships. In these situations,
source nodes typically have distinct biophysical properties from sinks. Due to
their ordered and unidirectional relationships, many such networks also have
hierarchical and multiscale structure. However, the majority of methods
performing node- and edge-level tasks in machine learning do not take these
properties into account, and thus have not been leveraged effectively for
scientific tasks such as cellular signaling network inference. We propose a new
framework called Directed Scattering Autoencoder (DSAE) which uses a directed
version of a geometric scattering transform, combined with the non-linear
dimensionality reduction properties of an autoencoder and the geometric
properties of the hyperbolic space to learn latent hierarchies. We show this
method outperforms numerous others on tasks such as embedding directed graphs
and learning cellular signaling networks.
