Jiang Bo, Wang Beibei, Tang Jin, Luo Bin
IEEE Trans Pattern Anal Mach Intell. 2022 Sep;44(9):4935-4947. doi: 10.1109/TPAMI.2021.3070599. Epub 2022 Aug 4.
Graph representation and learning is a fundamental problem in machine learning area. Graph Convolutional Networks (GCNs) have been recently studied and demonstrated very powerful for graph representation and learning. Graph convolution (GC) operation in GCNs can be regarded as a composition of feature aggregation and nonlinear transformation step. Existing GCs generally conduct feature aggregation on a full neighborhood set in which each node computes its representation by aggregating the feature information of all its neighbors. However, this full aggregation strategy is not guaranteed to be optimal for GCN learning and also can be affected by some graph structure noises, such as incorrect or undesired edge connections. To address these issues, we propose to integrate elastic net based selection into graph convolution and propose a novel graph elastic convolution (GeC) operation. In GeC, each node can adaptively select the optimal neighbors in its feature aggregation. The key aspect of the proposed GeC operation is that it can be formulated by a regularization framework, based on which we can derive a simple update rule to implement GeC in a self-supervised manner. Using GeC, we then present a novel GeCN for graph learning. Experimental results demonstrate the effectiveness and robustness of GeCN.
图表示与学习是机器学习领域的一个基本问题。图卷积网络（GCN）最近得到了研究，并在图表示与学习方面展现出强大的能力。GCN中的图卷积（GC）操作可被视为特征聚合和非线性变换步骤的组合。现有的GC通常在完整邻域集上进行特征聚合，其中每个节点通过聚合其所有邻居的特征信息来计算自身的表示。然而，这种全聚合策略对于GCN学习不一定是最优的，并且还可能受到一些图结构噪声的影响，例如不正确或不需要的边连接。为了解决这些问题，我们提议将基于弹性网络的选择集成到图卷积中，并提出一种新颖的图弹性卷积（GeC）操作。在GeC中，每个节点在其特征聚合过程中可以自适应地选择最优邻居。所提出的GeC操作的关键在于它可以由一个正则化框架来表述，基于此我们可以推导出一个简单的更新规则，以自监督的方式实现GeC。然后，使用GeC，我们提出了一种用于图学习的新颖的GeCN。实验结果证明了GeCN的有效性和鲁棒性。
