Graph convolutional networks (GCNs) allow us to learn topologically-aware node embeddings, which can be useful for classification or link prediction. However, by construction, they lack positional awareness and are unable to capture long-range dependencies without adding additional layers -- which in turn leads to over-smoothing and increased time and space complexity. Further, the complex dependencies between nodes make mini-batching challenging, limiting their applicability to large graphs. This paper proposes a Scalable Multi-resolution Graph Representation Learning (SMGRL) framework that enables us to learn multi-resolution node embeddings efficiently. Our framework is model-agnostic and can be applied to any existing GCN model. We dramatically reduce training costs by training only on a reduced-dimension coarsening of the original graph, then exploit self-similarity to apply the resulting algorithm at multiple resolutions. Inference of these multi-resolution embeddings can be distributed across multiple machines to reduce computational and memory requirements further. The resulting multi-resolution embeddings can be aggregated to yield high-quality node embeddings that capture both long- and short-range dependencies between nodes. Our experiments show that this leads to improved classification accuracy, without incurring high computational costs.

我们提出了一个可应用于任何现有GCN模型的可扩展多分辨率图表示学习(SMGRL)框架，通过学习多分辨率节点嵌入有效地捕获长和短距离依赖，并将其聚合以产生捕获高质量节点嵌入的优化算法，同时提高分类准确度，而不会产生高计算成本。

SMGRL: 可扩展的多分辨率图表示学习