Graph Pooling by Local Cluster Selection

TL;DR

The paper addresses graph pooling in graph neural networks by proposing Local Cluster Pooling (LCPool), a node-centered pooling framework that leverages local assignments and local clusters to adapt dropout sizes and strengthen connectivity. Central to LCPool is the Local Cluster Score MP (LCSMP), which learns node scores from both features and neighbor differences, and a pooling rule that selects top-scoring nodes while constructing a new adjacency via $A' = \text{ones}(A + A^2 + A^3)(\hat{i},\hat{i})$ or, more generally, via $A' = (S^T A S)(\hat{i},\hat{i})$. The framework unifies node selection and dense assignment under locality constraints, with Proposition 7 showing that the cluster function $v(\cdot)$ can be dismissed under common convolutions, and Lemma 5 guiding the simplified adjacency updates for unweighted graphs. Empirically, LCPool is competitive across hierarchical and plain GNN backbones on six graph classification datasets, often achieving the best average ranking and validating the proposed adaptive, sparse, and connectivity-boosting pooling approach. These findings suggest that local-cluster-based pooling can improve coarsening quality for downstream graph-level tasks while maintaining computational efficiency.

Abstract

Graph pooling is a family of operations which take graphs as input and produce shrinked graphs as output. Modern graph pooling methods are trainable and, in general inserted in Graph Neural Networks (GNNs) architectures as graph shrinking operators along the (deep) processing pipeline. This work proposes a novel procedure for pooling graphs, along with a node-centred graph pooling operator.

Figures (4)

• Figure 1: The figure shows how the adjacency matrix of pooled graph is calculated.
• Figure 2: $g^*(\cdot)$ can not distinct $x_0$ and $x'_0$ in the two local clusters above, since $x_0-x_3$ and $x_0-x_2$ cancels each other out.
• Figure 3: This figure shows the architecture of LCSMP. $L$ denotes the linear transformation, the unfilled circle denotes mathematical operation and filled cirecle denote the sum aggregation through neighbours. The subfigure 1 shows the overall structure of LCSMP from a message passing perspective. The subfigure 2 shows the message part of LCSMP. We calculate the differences and transform them with a linear layer. The subfigure 3 shows the aggregation part. The subfigure 4 shows how the importance score is learned from hidden features.
• Figure 4: The figure shows the architecture of GNN backbones. The top one is in hierarchical style and the bottom one in plain style. The grey shape denotes MLP, green shape denotes graph convolution operator, blue shape denotes graph pooling operator and unfilled shape denotes readout layer.