  With the remarkable success of representation learning in providing powerful
predictions and data insights, we have witnessed a rapid expansion of
representation learning techniques into modeling, analysis, and learning with
networks. Biomedical networks are universal descriptors of systems of
interacting elements, from protein interactions to disease networks, all the
way to healthcare systems and scientific knowledge. In this review, we put
forward an observation that long-standing principles of network biology and
medicine -- while often unspoken in machine learning research -- can provide
the conceptual grounding for representation learning, explain its current
successes and limitations, and inform future advances. We synthesize a spectrum
of algorithmic approaches that, at their core, leverage topological features to
embed networks into compact vector spaces. We also provide a taxonomy of
biomedical areas that are likely to benefit most from algorithmic innovation.
Representation learning techniques are becoming essential for identifying
causal variants underlying complex traits, disentangling behaviors of single
cells and their impact on health, and diagnosing and treating diseases with
safe and effective medicines.
