Depth-based subgraph convolutional auto-encoder for network representation learning

Zhihong Zhang, Dongdong Chen, Zeli Wang, Heng Li, Lu Bai, Edwin R. Hancock

Abstract: Highlights • To our knowledge, DS-CAE is the first convolution-based deep learning method for unsupervised network representation learning.Similar to the convolution for image processing, a subgraph-based convolution operation is proposed to scan a tree which is extracted from various graph structures. • In contrast to most existing models for unsupervised learning on graph-structured data, DS-CAE can capture highly non-linear network structure by simultaneously integrating raw node information and network structure into network representation learning. • Due to the deep representation, DS-CAE can map graphs to highly nonlinear deeply learned spaces to effectively preserve both the local and global information in original space. Abstract Network representation learning (NRL) aims to map vertices of a network into a low-dimensional space which preserves the network structure and its inherent properties. Most existing methods for network representation adopt shallow models which have relatively limited capacity to capture highly non-linear network structures, resulting in sub-optimal network representations. Therefore, it is nontrivial to explore how to effectively capture highly non-linear network structure and preserve the global and local structure in NRL. To solve this problem, in this paper we propose a new graph convolutional autoencoder architecture based on a depth-based representation of graph structure, referred to as the depth-based subgraph convolutional autoencoder (DS-CAE), which integrates both the global topological and local connectivity structures within a graph. Our idea is to first decompose a graph into a family of K-layer expansion subgraphs rooted at each vertex aimed at better capturing long-range vertex inter-dependencies. Then a set of convolution filters slide over the entire sets of subgraphs of a vertex to extract the local structural connectivity information. This is analogous to the standard convolution operation on grid data. In contrast to most existing models for unsupervised learning on graph-structured data, our model can capture highly non-linear structure by simultaneously integrating node features and network structure into network representation learning. This significantly improves the predictive performance on a number of benchmark datasets.