Research On Hyperbolic Graph Representation Learning Algorithm

Graphs are a universal language for describing and modeling complex systems.There is a lot of data in the real world that can be modeled via graphs,such as social networks,biological neuron networks,information networks,protein networks,transportation networks,etc.The problem of graph-based data mining has also attracted the attention of a large number of researchers.To analyze graphs better,more and more researchers study the problem of graph representation learning.In recent years,graph representation learning has also become a research hotspot in the field of graph data mining.Graph representation learning aims to map nodes and edges in a graph to a low-dimensional space while preserving the structure and properties of the graph.Most graph representation learning methods learn feature representations of graphs in Euclidean space,However,a fundamental problem is ignored by these graph representation learning methods:whether the Euclidean space are the appropriate space of graphs?Recently,some researchers have found that Euclidean graph representation learning could have a high distortion in the case of embedding graphs with treelikeness or hierarchical structure.To solve this problem,some graph representation learning methods try to use a non-Euclidean space,i.e.,hyperbolic space,to model graph data,and achieve good results.Therefore,hyperbolic graph representation learning has become a very promising research direction,and has received considerable research attention.As an emerging research topic,leveraging hyperbolic graph representation learning to obtain effective graph representations has become the key of research,and faces the following problems:(1)Since heterogeneous graphs contain rich semantic information,can we embed heterogeneous graphs in hyperbolic space to obtain more effective graph representations?(2)Since graph deep learning has more powerful ability in embedding graphs,can we design hyperbolic deep graph learning method to obtain more effective graph representations?(3)Since some hyperbolic graph operators are not well-defined,can we design more reasonable hyperbolic graph operators to obtain more effective graph representations?In addition,whether hyperbolic spaces can be applied in practical problems,such as recommendation,is also a research question worthy of attention.This paper focuses on hyperbolic graph representation learning,which aims to model the interactions in graphs in hyperbolic space.This paper will studies the problem of hyperbolic space heterogeneous graph embedding,hyperbolic graph attention neural network,Lorentzian graph neural networks,and hyperbolic graph representation learning in recommender systems.The main contributions of this paper are as follows:Firstly,for the applicability of heterogeneous graph,this paper analyzes the structure of heterogeneous graphs,and proposes a hyperbolic heterogeneous graph embedding model.Specifically,to capture the structural and semantic relationships between nodes,we use meta-path-guided random walks to sample node sequences.Then,we use hyperbolic distance to measure the similarities between nodes in heterogeneous graphs.Finally,we further derive optimization strategies to update the parameters in the proposed model.The experimental results demonstrate the effectiveness of the proposed model.Secondly,for the adaptability of deep learning,this paper designs some hyperbolic graph operators,and proposes a hyperbolic graph deep learning model,i.e.,hyperbolic graph attention neural network.The proposed model uses the gyrovector space as an elegant algebraic formalism for hyperbolic space.The matrix-vector multiplication in the gyrovector space is used to transform the graph features.Also,the product of hyperbolic spaces is used to design hyperbolic multi-head attention mechanism.Furthermore,the proposed model uses logarithmic map and exponential map to ensure the efficiency of the proposed model.The experimental results demonstrate the effectiveness of the proposed model.Thirdly,for the rationality of hyperbolic operators,this work finds some hyperbolic graph operators are not well defined,and proposes Lorentzian graph convolutional network,which leverages some redefined hyperbolic graph operators.Specifically,this paper redefines a series of hyperbolic graph operators,such as feature transformations and nonlinear activations.Also,an elegant neighborhood aggregation method is designed based on the centroid of Lorentzian distance.Furthermore,this paper proves that some proposed graph operations are equivalent in different type of hyperbolic geometries,which fundamentally demonstrates the correctness of the proposed hyperbolic operators.Experimential results show that the proposed method outperforms the state-ofthe-art.Fourthly,in order to verify the effectiveness of hyperbolic graph representation learning in recommender systems,this paper proposes a geometric disentangled collaborate filtering method.Specifically,since there are multiple latent non-Euclidean characteristics between users and items in recommendation,this paper learns geometric disentanged representations by modeling useritem interactions and capturing multiple geometric characteristics related latent intent information.Experimental results demonstrate the effectiveness of the proposed model.