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Deep Learning over Hypergraphs

Series: Ph.D (Engg.)Thesis Defence -ON-LINE

Speaker: Mr. Naganand Yadati, Ph.D (Engg.) Student Dept. of CSA

Date/Time: Dec 14 09:00:00

Location: Microsoft Teams - ON-LINE

Faculty Advisor: Prof. Partha Pratim Talukdar

Though graphs have been extensively used for modelling real-world relational datasets, they are restricted to pairwise relationships, i.e., each edge connects exactly two vertices. Many real-world relational datasets such as academic networks, chemical reaction networks, email communication networks contain group-wise relationships that go beyond pairwise associations. Hypergraphs can flexibly model such datasets by relaxing the notion of an edge to connect an arbitrary number of vertices and providing a mathematical foundation for understanding and learning from large amounts of real-world heterogeneous data.
The state-of-the-art techniques for learning from graph data with pairwise relationships use graph-based deep learning models such as graph neural networks. A prominent observation that inspires this thesis is that deep neural networks are still under-explored for hypergraph data with group-wise relationships. Hypergraphs have been utilised as primary data structures in many machine learning tasks such as vertex classification, hypergraph link prediction, and knowledge base completion. However, the fundamental limitation of most existing non-neural techniques is that they cannot leverage high-dimensional features on vertices, especially those which are not present in relational data (e.g., text attributes of documents in academic networks). In this thesis, we propose novel deep learning-based methods for hypergraph data with high dimensional vertex features.
1) Deep Learning for Hypergraph Vertex-level Predictions In the first part of the thesis, we focus on addressing limitations of existing methods for vertex-level tasks over hypergraphs. In particular, we propose HyperGraph Convolutional Network (HyperGCN) for semi-supervised vertex classification over hypergraphs. Unlike existing methods, HyperGCN principally bridges tools from graph neural networks and spectral hypergraph theory.
2) Deep Learning for Hypergraph Link Prediction In the second part, we focus on the task of predicting groupwise relationships (i.e., link prediction over hypergraphs). We propose Neural Hyperlink Predictor (NHP), a novel neural network-based method for link prediction over hypergraphs. NHP uses a novel scoring layer that principally enables us to predict group relationships on incomplete hypergraphs where hyperedges need not represent similarity.
3) Deep Learning for Multi-Relational and Recursive Hypergraphs In the third and final part, we explore more complex structures such as multi-relational hypergraphs in which each hyperedge is typed (i.e., belongs to a relation type) and recursive hypergraphs in which hyperedges can act as vertices in other hyperedges. We first propose Generalised Message Passing Neural Network (G-MPNN) for learning vertex representations on multi-relational ordered hypergraphs. G-MPNN generalises existing MPNNs on graphs, hypergraphs, multi-relational graphs, heterogeneous graphs, and multi-layer networks. We then propose MPNN-Recursive, a novel framework, to handle recursively structured data. Extensive experimentation on real-world hypergraphs shows the effectiveness of our proposed models.

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