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.
There are three main approaches for solving the graph classification problem. The most common approach is concerned with building graph kernels. In graph kernels, a graph @math is decomposed into (possibly different) @math sub-structures. The graph kernel @math is defined based on the frequency of each sub-structure appeared in @math and @math , respectively. Namely, @math , where @math is the vector containing frequencies of @math sub-structures, and @math is an inner product in an appropriately defined normed vector space. Much of work has been devoted to deciding on which sub-structures are more suitable than others. Among the existing graph kernels, popular ones are graphlets @cite_0 @cite_35 , random walk and shortest path kernels @cite_9 @cite_13 , and Weisfeiler-Lehman subtree kernel @cite_17 . Furthermore, deep graph kernels @cite_18 , graph invariant kernels @cite_20 , optimal assignment graph kernels @cite_1 and multiscale laplacian graph kernel @cite_32 have been proposed with the goal to re-define kernel functions to appropriately capture sub-structural similarity at different levels. Another line of research in this area focuses on efficiently computing these kernels either through exploiting certain structure dependency, or via approximation or randomization @cite_26 @cite_40 @cite_2 .
@cite_35 @cite_18 @cite_26 @cite_9 @cite_1 @cite_32 @cite_0 @cite_40 @cite_2 @cite_13 @cite_20 @cite_17
2280799770 2008857988 1495400410 2950656243
We introduce a novel kernel that upgrades the Weisfeiler-Lehman and other graph kernels to effectively exploit high-dimensional and continuous vertex attributes. Graphs are first decomposed into subgraphs. Vertices of the subgraphs are then compared by a kernel that combines the similarity of their labels and the similarity of their structural role, using a suitable vertex invariant. By changing this invariant we obtain a family of graph kernels which includes generalizations of Weisfeiler-Lehman, NSPDK, and propagation kernels. We demonstrate empirically that these kernels obtain state-of-the-art results on relational data sets. In this paper, we present Deep Graph Kernels, a unified framework to learn latent representations of sub-structures for graphs, inspired by latest advancements in language modeling and deep learning. Our framework leverages the dependency information between sub-structures by learning their latent representations. We demonstrate instances of our framework on three popular graph kernels, namely Graphlet kernels, Weisfeiler-Lehman subtree kernels, and Shortest-Path graph kernels. Our experiments on several benchmark datasets show that Deep Graph Kernels achieve significant improvements in classification accuracy over state-of-the-art graph kernels. Typical graph-theoretic approaches for semi-supervised classification infer labels of unlabeled instances with the help of graph Laplacians. Founded on the spectral decomposition of the graph Laplacian, this paper learns a kernel matrix via minimizing the leave-one-out classification error on the labeled instances. To this end, an efficient algorithm is presented based on linear programming, resulting in a transductive spectral kernel. The idea of our algorithm stems from regularization methodology and also has a nice interpretation in terms of spectral clustering. A simple classifier can be readily built upon the learned kernel, which suffices to give prediction for any data point aside from those in the available dataset. Besides this usage, the spectral kernel can be effectively used in tandem with conventional kernel machines such as SVMs. We demonstrate the efficacy of the proposed algorithm through experiments carried out on challenging classification tasks. Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG kernels) that we define in this paper can account for structure at a range of different scales. At the heart of the MLG construction is another new graph kernel, called the Feature Space Laplacian Graph kernel (FLG kernel), which has the property that it can lift a base kernel defined on the vertices of two graphs to a kernel between the graphs. The MLG kernel applies such FLG kernels to subgraphs recursively. To make the MLG kernel computationally feasible, we also introduce a randomized projection procedure, similar to the Nystr "om method, but for RKHS operators.