  Recently, Graph Convolutional Networks (GCNs) have proven to be a powerful
machine learning tool for Computer-Aided Diagnosis (CADx) and disease
prediction. A key component in these models is to build a population graph,
where the graph adjacency matrix represents pair-wise patient similarities.
Until now, the similarity metrics have been defined manually, usually based on
meta-features like demographics or clinical scores. The definition of the
metric, however, needs careful tuning, as GCNs are very sensitive to the graph
structure. In this paper, we demonstrate for the first time in the CADx domain
that it is possible to learn a single, optimal graph towards the GCN's
downstream task of disease classification. To this end, we propose a novel,
end-to-end trainable graph learning architecture for dynamic and localized
graph pruning. Unlike commonly employed spectral GCN approaches, our GCN is
spatial and inductive, and can thus infer previously unseen patients as well.
We demonstrate significant classification improvements with our learned graph
on two CADx problems in medicine. We further explain and visualize this result
using an artificial dataset, underlining the importance of graph learning for
more accurate and robust inference with GCNs in medical applications.
