Neural Gaussian Similarity Modeling for Differential Graph Structure Learning
This work addresses a gradient flow problem in graph structure learning for domains with graph-unknown non-Euclidean data, representing an incremental improvement.
The paper tackles the challenge of gradient flow obstruction in end-to-end graph structure learning by introducing a differentiable sampling method using the reparameterization trick, and proposes Neural Gaussian Similarity to sample non-nearest neighbors, achieving effective results in experiments.
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.