Quantifying the Alignment of Graph and Features in Deep Learning
This work addresses the challenge of interpreting and improving GCNs for researchers and practitioners, but it is incremental as it builds on existing alignment concepts without introducing a new method.
The paper tackles the problem of understanding classification performance in graph convolutional networks by quantifying the alignment between features, graph structure, and ground truth using a subspace alignment measure (SAM). The result shows that SAM correlates with performance, as demonstrated through limiting cases, randomizations, and examples like citation networks, revealing the relative importance of graph and features.
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.