Drug repositioning is an attractive cost-efficient strategy for the
development of treatments for human diseases. Here, we propose an interpretable
model that learns disease self-representations for drug repositioning. Our
self-representation model represents each disease as a linear combination of a
few other diseases. We enforce proximity in the learnt representations in a way
to preserve the geometric structure of the human phenome network - a
domain-specific knowledge that naturally adds relational inductive bias to the
disease self-representations. We prove that our method is globally optimal and
show results outperforming state-of-the-art drug repositioning approaches. We
further show that the disease self-representations are biologically
interpretable.