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-the-art algorithms.Comment: 10 pages, 3 figures, ICCV 2019 accepte