  The paper discusses a pooling mechanism to induce subsampling in graph
structured data and introduces it as a component of a graph convolutional
neural network. The pooling mechanism builds on the Non-Negative Matrix
Factorization (NMF) of a matrix representing node adjacency and node similarity
as adaptively obtained through the vertices embedding learned by the model.
Such mechanism is applied to obtain an incrementally coarser graph where nodes
are adaptively pooled into communities based on the outcomes of the
non-negative factorization. The empirical analysis on graph classification
benchmarks shows how such coarsening process yields significant improvements in
the predictive performance of the model with respect to its non-pooled
counterpart.
