Various Graph Neural Networks (GNNs) have been successful in analyzing data
in non-Euclidean spaces, however, they have limitations such as oversmoothing,
i.e., information becomes excessively averaged as the number of hidden layers
increases. The issue stems from the intrinsic formulation of conventional graph
convolution where the nodal features are aggregated from a direct neighborhood
per layer across the entire nodes in the graph. As setting different number of
hidden layers per node is infeasible, recent works leverage a diffusion kernel
to redefine the graph structure and incorporate information from farther nodes.
Unfortunately, such approaches suffer from heavy diagonalization of a graph
Laplacian or learning a large transform matrix. In this regards, we propose a
diffusion learning framework, where the range of feature aggregation is
controlled by the scale of a diffusion kernel. For efficient computation, we
derive closed-form derivatives of approximations of the graph convolution with
respect to the scale, so that node-wise range can be adaptively learned. With a
downstream classifier, the entire framework is made trainable in an end-to-end
manner. Our model is tested on various standard datasets for node-wise
classification for the state-of-the-art performance, and it is also validated
on a real-world brain network data for graph classifications to demonstrate its
practicality for Alzheimer classification.

基于扩散核的扩散学习框架在图神经网络中控制了特征聚合范围，解决了节点级分类和过度平滑化的问题，并具备在阿尔茨海默病分类中实际应用的可行性。

学习在图上近似自适应核卷积

Learning to Approximate Adaptive Kernel Convolution on Graphs

Disease gene prioritization assigns scores to genes or proteins according to
their likely relevance for a given disease based on a provided set of seed
genes. Here, we describe a new algorithm for disease gene prioritization based
on continuous-time quantum walks using the adjacency matrix of a
protein-protein interaction (PPI) network. Our algorithm can be seen as a
quantum version of a previous method known as the diffusion kernel, but,
importantly, has higher performance in predicting disease genes, and also
permits the encoding of seed node self-loops into the underlying Hamiltonian,
which offers yet another boost in performance. We demonstrate the success of
our proposed method by comparing it to several well-known gene prioritization
methods on three disease sets, across seven different PPI networks. In order to
compare these methods, we use cross-validation and examine the mean reciprocal
ranks and recall values. We further validate our method by performing an
enrichment analysis of the predicted genes for coronary artery disease. We also
investigate the impact of adding self-loops to the seeds, and argue that they
allow the quantum walker to remain more local to low-degree seed nodes.

基于连续时间量子行走和蛋白质相互作用网络的新算法进行了疾病基因优先排序，通过给定的种子基因对基因或蛋白质进行得分评估，该算法具有比现有方法更高的预测疾病基因的性能，并且允许在底层哈密尔顿变换中对种子节点进行自循环的编码，进一步提高性能。