  Learning on graph structured data has drawn increasing interest in recent
years. Frameworks like Graph Convolutional Networks (GCNs) have demonstrated
their ability to capture structural information and obtain good performance in
various tasks. In these frameworks, node aggregation schemes are typically used
to capture structural information: a node's feature vector is recursively
computed by aggregating features of its neighboring nodes. However, most of
aggregation schemes treat all connections in a graph equally, ignoring node
feature similarities. In this paper, we re-interpret node aggregation from the
perspective of kernel weighting, and present a framework to consider feature
similarity in an aggregation scheme. Specifically, we show that normalized
adjacency matrix is equivalent to a neighbor-based kernel matrix in a Krein
Space. We then propose feature aggregation as the composition of the original
neighbor-based kernel and a learnable kernel to encode feature similarities in
a feature space. We further show how the proposed method can be extended to
Graph Attention Network (GAT). Experimental results demonstrate better
performance of our proposed framework in several real-world applications.
