Graph Representation Learning With Neural Network In Hyperbolic Spacey

Machine learning attempts to use graph structured data as feature information for predicting or discovering new patterns.The focus of research is on discrete nodes in graph embedded into continuous space with certain required geometric properties.Although the graph representation learning shows great potential,embedding the graph into a low-dimensional space is not a simple task.The focus of this paper is to give the neural network the appropriate geometric structure to capture the basic properties of the graph data,especially the hierarchy and clustering behavior.The heterogeneous and strong clustering topological properties in complex networks are surprisingly reflected in the basic properties of hyperbolic negative curvature space.Therefore,the purpose of this paper is to learn the low-dimensional compact node feature representation by modeling the interaction or relationship that use the neural network and the hyperbolic manifold metric structure,and then explore whether hyperbolic space can help to learn the embedding of graph data.This paper fuses the rich hierarchical structure of graph with the continuous representation supported by modern machine learning,and it respectively proposed The Generative Adversarial Graph Representation Learning in Poincaré Model and The Neural Ranking Graph Representation Learning in Hyperboloid Model to capture the potential feature representation of graph.Especially,they both use unsupervised end-to-end method of neural networks and hierarchical selforganization ability of hyperbolic geometry to automatically extract the information of node similarity and hierarchy.(1)The Generative Adversarial Graph Representation Learning in Poincaré Model,it explicitly captures the hierarchical features of the data in the embedding space by setting the distance metric to the distance function in the Poincaré hyperbolic geometric model.At the same time,the method combines the advanced random walk strategy with exploring the remote topology information of the graph to construct the dataset required for training and utilizes the principle of adversarial learning in neural network to automatically obtain higher-level node feature representation.The designed neural network alternately boosts the performance by competing between the generative model and the adversarial model,and adopts a powerful learning optimization strategy to improve the efficiency of the model,so that it can produce higher quality node feature representation.Then,the learned node feature vector representation is applied to node classification,link prediction and visualization.Moreover,the dimensional sensitivity of the model is analyzed.The experimental results show that the method has good expressiveness and effectiveness in multiple tasks.(2)Inspired by some recently proposed hyperbolic spaces provide strong representations of entailment,The Neural Ranking Graph Representation Learning in Hyperboloid Model does not use an excessively complex node interaction mechanism,but instead designs a smaller and faster neural ranking model with embedding hyperbolic geometry to capture topology information for graph data.It uses Bayesian Personalized Ranking to maximize the gap between the correct links and the wrong links for automatically learning the similarity of the nodes.In order to capture the hierarchical feature information of the data,in particularly,the hyperbolic layer of the neural network model calculates the hierarchical distance score of the nodes with the distance function in the hyperboloid model.Finally,the model uses the Gradient Descent on Riemannian to learn the low-dimensional compact feature vector of nodes.After obtaining the potential feature vector representation of the node,this paper compares the graph representation learning methods in different spaces for the node recommendation and node classification tasks,and analyzes the sensitivity of the proposed method to the dimension and the convergence of the model.The experimental results show that the proposed method is not only efficient but also can get more compact and more expressive feature vector representation in node feature learning.In summary,this paper introduces the hyperbolic geometric metrics in the neural network model to learn the topological features of the nodes in graph,and shows how they can efficiently learn the similarity and hierarchy of nodes to provide a transcendental advantages of Euclidean embedding.Many experimental results show that the proposed methods are not only efficient in node feature learning but also can obtain more compact and more expressive feature vector representation.Moreover,it shows that learning meaningful graph representation can benefit many important graph analysis tasks,and the hierarchy embedded in hyperbolic space correspond well to the underlying semantics of data.