  We show that the classification performance of graph convolutional networks
(GCNs) is related to the alignment between features, graph, and ground truth,
which we quantify using a subspace alignment measure (SAM) corresponding to the
Frobenius norm of the matrix of pairwise chordal distances between three
subspaces associated with features, graph, and ground truth. The proposed
measure is based on the principal angles between subspaces and has both
spectral and geometrical interpretations. We showcase the relationship between
the SAM and the classification performance through the study of limiting cases
of GCNs and systematic randomizations of both features and graph structure
applied to a constructive example and several examples of citation networks of
different origins. The analysis also reveals the relative importance of the
graph and features for classification purposes.
