Density-aware Local Siamese Autoencoder Network Embedding with Autoencoder Graph Clustering

Network embedding aims to learn latent low dimensional representation of vertices in graphs while preserving the intrinsic characteristics of graph data. In this paper, we propose a density-aware local autoencoder embedding architecture, DAL-SAE, with three features. First, we develop a flexible density-aware local deep autoencoder embedding method to perform local embedding on each of K clustering-based subgraphs with the optimization at both vertex and subgraph levels, in response to imbalanced density-based local characteristics of vertices and subgraphs. We design K local autoencoder embedding models, each with individual parameters and structure, to jointly train K subgraphs and optimize the loss functions within and across clusters. Second, we design an autoencoder graph clustering method to optimize local embedding and graph clustering simultaneously and capture local, clustering, and global network structure in the learning process. Third but last, a density-aware local Siamese autoencoder embedding approach can be utilized to train multiple clustering-based subgraphs with similar local characteristics on the common Siamese networks, to save the memory consumption of multiple local embedding models as well as maintain the similar embedding features.