Graph Convolutional Neural Networks (GCNNs) are the most recent exciting advancement in deep learning field and their applications are quickly spreading in multi-cross-domains including bioinformatics, chemoinformatics, social networks, natural language processing and computer vision. In this paper, we expose and tackle some of the basic weaknesses of a GCNN model with a capsule idea presented in hinton2011transforming and propose our Graph Capsule Network (GCAPS-CNN) model. In addition, we design our GCAPS-CNN model to solve especially graph classification problem which current GCNN models find challenging. Through extensive experiments, we show that our proposed Graph Capsule Network can significantly outperforms both the existing state-of-art deep learning methods and graph kernels on graph classification benchmark datasets.
Current graph kernels suffer from two limitations: graph kernels based on counting particular types of subgraphs ignore the relative position of these subgraphs to each other, while graph kernels based on algebraic methods are limited to graphs without node labels. In this paper we present the graphlet spectrum, a system of graph invariants derived by means of group representation theory that capture information about the number as well as the position of labeled subgraphs in a given graph. In our experimental evaluation the graphlet spectrum outperforms state-of-the-art graph kernels. For the purpose of learning on graphs, we hunt for a graph feature representation that exhibit certain uniqueness, stability and sparsity properties while also being amenable to fast computation. This leads to the discovery of family of graph spectral distances (denoted as FGSD) and their based graph feature representations, which we prove to possess most of these desired properties. To both evaluate the quality of graph features produced by FGSD and demonstrate their utility, we apply them to the graph classification problem. Through extensive experiments, we show that a simple SVM based classification algorithm, driven with our powerful FGSD based graph features, significantly outperforms all the more sophisticated state-of-art algorithms on the unlabeled node datasets in terms of both accuracy and speed; it also yields very competitive results on the labeled datasets - despite the fact it does not utilize any node label information. The central issue in representing graph-structured data instances in learning algorithms is designing features which are invariant to permuting the numbering of the vertices. We present a new system of invariant graph features which we call the skew spectrum of graphs. The skew spectrum is based on mapping the adjacency matrix of any (weigted, directed, unlabeled) graph to a function on the symmetric group and computing bispectral invariants. The reduced form of the skew spectrum is computable in O(n3) time, and experiments show that on several benchmark datasets it can outperform state of the art graph kernels.