Neural Gaussian Similarity Modeling for Differential Graph Structure
  Learning
Xiaolong Fan Maoguo Gong Yue Wu Zedong Tang Jieyi Liu
Graph Structure Learning (GSL) has demonstrated considerable potential in the
analysis of graph-unknown non-Euclidean data across a wide range of domains.
However, constructing an end-to-end graph structure learning model poses a
challenge due to the impediment of gradient flow caused by the nearest neighbor
sampling strategy. In this paper, we construct a differential graph structure
learning model by replacing the non-differentiable nearest neighbor sampling
with a differentiable sampling using the reparameterization trick. Under this
framework, we argue that the act of sampling \mbox{nearest} neighbors may not
invariably be essential, particularly in instances where node features exhibit
a significant degree of similarity. To alleviate this issue, the bell-shaped
Gaussian Similarity (GauSim) modeling is proposed to sample non-nearest
neighbors. To adaptively model the similarity, we further propose Neural
Gaussian Similarity (NeuralGauSim) with learnable parameters featuring flexible
sampling behaviors. In addition, we develop a scalable method by transferring
the large-scale graph to the transition graph to significantly reduce the
complexity. Experimental results demonstrate the effectiveness of the proposed
methods.