### Abstract

Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However, most of the existing graph neural networks suffer from the following limitations: (1) there is limited analysis regarding the graph convolution properties, such as seed-oriented, degree-aware and order-free; (2) the node's degree-specific graph structure is not explicitly expressed in graph convolution for distinguishing structure-aware node neighborhoods; (3) the theoretical explanation regarding the graph-level pooling schemes is unclear. To address these problems, we propose a generic degree-specific graph neural network named DEMO-Net motivated by Weisfeiler-Lehman graph isomorphism test that recursively identifies 1-hop neighborhood structures. In order to explicitly capture the graph topology integrated with node attributes, we argue that graph convolution should have three properties: seed-oriented, degree-aware, order-free. To this end, we propose multi-task graph convolution where each task represents node representation learning for nodes with a specific degree value, thus leading to preserving the degree-specific graph structure. In particular, we design two multi-task learning methods: degree-specific weight and hashing functions for graph convolution. In addition, we propose a novel graph-level pooling/readout scheme for learning graph representation provably lying in a degree-specific Hilbert kernel space. The experimental results on several node and graph classification benchmark data sets demonstrate the effectiveness and efficiency of our proposed DEMO-Net over state-of-the-art graph neural network models.

Original language | English (US) |
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Title of host publication | KDD 2019 - Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining |

Publisher | Association for Computing Machinery |

Pages | 406-415 |

Number of pages | 10 |

ISBN (Electronic) | 9781450362016 |

DOIs | |

State | Published - Jul 25 2019 |

Externally published | Yes |

Event | 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2019 - Anchorage, United States Duration: Aug 4 2019 → Aug 8 2019 |

### Publication series

Name | Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining |
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### Conference

Conference | 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2019 |
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Country | United States |

City | Anchorage |

Period | 8/4/19 → 8/8/19 |

### Keywords

- Degree-specific Convolution
- Graph Isomorphism Test
- Graph Neural Network
- Multi-task Learning

### ASJC Scopus subject areas

- Software
- Information Systems

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## Cite this

*KDD 2019 - Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining*(pp. 406-415). (Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining). Association for Computing Machinery. https://doi.org/10.1145/3292500.3330950