SSHPool: The Separated Subgraph-based Hierarchical Pooling

TL;DR

The paper addresses over-smoothing and degradation in hierarchical graph pooling by introducing SSHPool, which partitions each graph layer into separated subgraphs using a hard assignment $S^{(l)}$ derived from $S_{ ext{soft}}^{(l)} = \text{softmax}(X^{(l)})$ with assignment ratio $\alpha = n_{l+1}/n_l$, and applies per-subgraph local convolutions to produce $Z^{(l)}_j$. The layer coarsening yields $X^{(l+1)} = \|_{j=1}^{n_{l+1}} \hat{s}^{(l)\top}_j Z^{(l)}_j$ and $A^{(l+1)} = S^{(l)\top} A^{(l)} S^{(l)}$, enabling hierarchical feature extraction across layers. An end-to-end GNN framework combines an initial global convolution (e.g., DGCNN) with SSHPool layers and a Graph Attention Layer defined by $\mathcal{A}= \mathrm{Attention}(X^{(0)}, X) = \mathrm{softmax}\left(\frac{(X W_q)(X^{(0)} W_k)^{\top}}{\sqrt{d}}\right) (X^{(0)} W_v)$ to fuse features for classification by an MLP. Empirical results on seven standard graph datasets show SSHPool-based models achieve state-of-the-art performance, validating its ability to mitigate over-smoothing while capturing rich hierarchical graph structure.

Abstract

In this paper, we develop a novel local graph pooling method, namely the Separated Subgraph-based Hierarchical Pooling (SSHPool), for graph classification. We commence by assigning the nodes of a sample graph into different clusters, resulting in a family of separated subgraphs. We individually employ the local graph convolution units as the local structure to further compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. Since these subgraphs are separated by different clusters and the structural information cannot be propagated between them, the local convolution operation can significantly avoid the over-smoothing problem caused by message passing through edges in most existing Graph Neural Networks (GNNs). By hierarchically performing the proposed procedures on the resulting coarsened graph, the proposed SSHPool can effectively extract the hierarchical global features of the original graph structure, encapsulating rich intrinsic structural characteristics. Furthermore, we develop an end-to-end GNN framework associated with the SSHPool module for graph classification. Experimental results demonstrate the superior performance of the proposed model on real-world datasets.

Figures (5)

• Figure 1: Descriptions of two pooling methods. Both the global and the local pooling methods convert the original input graph into the global feature. On the left side, the global pooling tends to directly sum up or average the representations of all nodes over the whole graph structure. By contrast, on the right side, the local pooling tends to assigns the nodes into different clusters, and then hierarchically aggregates the nodes from the same cluster into a coarsened node, resulting in a family of layer-wise coarsened graphs.
• Figure 2: The computational architecture for the proposed SSHPool of each layer. The first step is the assignment where the input graph is decomposed into multiple separated subgraphs. Then, the second one is the coarsening process where these subgraphs are compressed into the nodes of the coarsened graph.
• Figure 3: The computational architecture of our GNN framework.
• Figure 4: Analysis with the depth.
• Figure 5: Analysis with the assignment ratio.