Graph Autoencoders with Deconvolutional Networks

Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a low pass filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional Networks (GDNs) that reconstruct graph signals from smoothed node representations. We motivate the design of Graph Deconvolutional Networks via a combination of inverse filters in spectral domain and de-noising layers in wavelet domain, as the inverse operation results in a high pass filter and may amplify the noise. Based on the proposed GDN, we further propose a graph autoencoder framework that first encodes smoothed graph representations with GCN and then decodes accurate graph signals with GDN. We demonstrate the effectiveness of the proposed method on several tasks including unsupervised graph-level representation, social recommendation and graph generation. Autoencoders have demonstrated excellent performance on tasks such as unsupervised representation learning (Bengio, 2009) and de-noising (Vincent et al., 2010). Recently, several studies (Zeiler & Fergus, 2014; Long et al., 2015) have demonstrated that the performance of autoencoders can be further improved by encoding with Convolutional Networks and decoding with Deconvolutional Networks (Zeiler et al., 2010). Notably, Noh et al. (2015) present a novel symmetric architecture that provides a bottom-up mapping from input signals to latent hierarchical feature space with {convolution, pooling} operations and then maps the latent representation back to the input space with {deconvolution, unpooling} operations. While this architecture has been successful when processing features with structures existed in the Euclidean space (e.g., images), recently there has been a surging interest in applying such a framework on non-Euclidean data like graphs.