Interpretable Sparsification of Brain Graphs: Better Practices and
  Effective Designs for Graph Neural Networks
Gaotang Li Marlena Duda Xiang Zhang Danai Koutra Yujun Yan
Brain graphs, which model the structural and functional relationships between
brain regions, are crucial in neuroscientific and clinical applications
involving graph classification. However, dense brain graphs pose computational
challenges including high runtime and memory usage and limited
interpretability. In this paper, we investigate effective designs in Graph
Neural Networks (GNNs) to sparsify brain graphs by eliminating noisy edges.
While prior works remove noisy edges based on explainability or task-irrelevant
properties, their effectiveness in enhancing performance with sparsified graphs
is not guaranteed. Moreover, existing approaches often overlook collective edge
removal across multiple graphs.
  To address these issues, we introduce an iterative framework to analyze
different sparsification models. Our findings are as follows: (i) methods
prioritizing interpretability may not be suitable for graph sparsification as
they can degrade GNNs' performance in graph classification tasks; (ii)
simultaneously learning edge selection with GNN training is more beneficial
than post-training; (iii) a shared edge selection across graphs outperforms
separate selection for each graph; and (iv) task-relevant gradient information
aids in edge selection. Based on these insights, we propose a new model,
Interpretable Graph Sparsification (IGS), which enhances graph classification
performance by up to 5.1% with 55.0% fewer edges. The retained edges identified
by IGS provide neuroscientific interpretations and are supported by
well-established literature.