Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning

Abstract

We propose a symmetric graph convolutional autoencoder which produces a low-dimensional latent representation from a graph. In contrast to the existing graph autoencoders with asymmetric decoder parts, the proposed autoencoder has a newly designed decoder which builds a completely symmetric autoencoder form. For the reconstruction of node features, the decoder is designed based on Laplacian sharpening as the counterpart of Laplacian smoothing of the encoder, which allows utilizing the graph structure in the whole processes of the proposed autoencoder architecture. In order to prevent the numerical instability of the network caused by the Laplacian sharpening introduction, we further propose a new numerically stable form of the Laplacian sharpening by incorporating the signed graphs. In addition, a new cost function which finds a latent representation and a latent affinity matrix simultaneously is devised to boost the performance of image clustering tasks. The experimental results on clustering, link prediction and visualization tasks strongly support that the proposed model is stable and outperforms various state-of-theart algorithms.

Adaptive Graph Encoder for Attributed Graph Embedding

“…GALA [24] proposes a symmetric graph convolutional autoencoder recovering the feature matrix. The encoder is based on Laplacian smoothing while the decoder is based on Laplacian sharpening.…”

“…[32] leverages marginalized denoising autoencoder to disturb the structure information. To build a symmetric graph autoencoder, [24] proposes Laplacian sharpening as the counterpart of Laplacian smoothing in the encoder. The authors claim that Laplacian sharpening is a process that makes the reconstructed feature of each node away from the centroid of its neighbors to avoid over-smoothing.…”

MORONET: Multi-omics Integration via Graph Convolutional Networks for Biomedical Data Classification

“…4 is tuned over {1, 2, 5, 10} through cross validation, and the same k value is adopted across all experiments on the same dataset. Although GCN has been widely-utilized in unsupervised [59][60][61][62] and semi-supervised 58,[63][64][65] learning, in this paper, we further extend the use of GCN for supervised classification tasks. For training data X X X tr ∈ R n tr ×d , the corresponding adjacency matrix…”

Filter Pruning and Re-Initialization via Latent Space Clustering

“…The next step is to embed V into latent space based on G. This requires a specific unsupervised graph representation learning technique. We adopt one of the SOTA methods, i.e., graph convolutional autoencoder using Laplacian smoothing and sharpening (GALA) [25]. Fig.…”

“…In specific, our method defines filters and feature maps generated by the filters as vertices and edges to be a graph encoding the relationships between filters as well as their responses. We employ a graph convolution encoder [25] to transform filter relation graph into a latent space where the latent filter features are clustered. As shown in Fig.…”