MatPool: Matrix-pattern-oriented Pooling for Graph Property Prediction

Zonghai Zhu, Ying Huang, Huanlai Xing, Li Feng, Yuge Xu

Keywords: Graph Pooling, Matrix-Pattern-Oriented, Matrix Neural Network, Graph Neural Network

Abstract: Graph property prediction usually involves using a model to predict the label for the entire graph, which often has complex structures. Because input graphs have different sizes, current methods generally use graph pooling to coarsen them into a graph-level representation with a unified vector pattern. However, this coarsening process can lead to a significant loss of graph information. In this work, we explore the graph representation by using a matrix pattern and introduce an algorithm called Matrix-pattern-oriented Pooling (MatPool) that provides a unified graph-level representation for different graphs. MatPool multiplies the transposed feature matrix by the feature matrix itself and then conducts an isomorphic mapping to create a Matrix Representation (MR) that preserves the graph information and satisfies permutation invariance. Since the multiplication operation calculates the relationships between each feature, MR exhibits row-column correlations under the matrix pattern. To match this correlation, MatPool uses a novel and efficient Matrix Neural Network (MNN) with two-sided weight matrices to match the row-column correlation under the matrix pattern. We provide theoretical analyses to reveal the properties of MatPool and explain why it can preserve graph information and satisfy the permutation invariance. Extensive experiments on various graph property prediction benchmarks show the efficiency and effectiveness of MatPool.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 6707