R-convolution graph kernels are positive-semidefinite functions that decompose graphs into substructures and compare them. One problem in the effective implementation of this idea is that the substructures are not independent, which leads to high-dimensional feature space. In addition, graph kernels cannot capture the high-order complex interactions between vertices. To mitigate these two problems, we propose a framework called DeepMap to learn deep representations for graph feature maps used in graph kernels. The learned deep representation for a graph is a dense and low-dimensional vector that captures complex high-order interactions in a vertex neighborhood. We empirically validate DeepMap on various graph classification benchmarks and demonstrate that it achieves state-of-the-art performance.

Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into substructures and compare them. One problem in the effective implementation of this idea is that the substructures are not independent, which leads to high-dimensional feature space. In addition, graph kernels cannot capture the high-order complex interactions between vertices. To mitigate these two problems, we propose a framework calledDeepMapto learn deep representations for graph feature maps. The learned deep representation for a graph is a dense and low-dimensional vector that captures complex high-order interactions in a vertex neighborhood.DeepMapextends Convolutional Neural Networks (CNNs) to arbitrary graphs by generating aligned vertex sequences and building the receptive field for each vertex. We empirically validateDeepMapon various graph classification benchmarks and demonstrate that it achieves state-of-the-art performance.

In many real-world big data applications, the data distribution is not homogeneous over entire data, but instead varies across groups/clusters of data samples. Although a model's predictive performance remains vital, there is also a need to learn succinct sets of features that evolve and capture smooth variations in data distribution. These small sets of features not only lead to high prediction accuracy, but also discover the important underlying processes. We investigate this challenging problem by developing a novel multi-task learning paradigm that trains multiple support vector machine (SVM) classifiers over a set of related data clusters, and directly imposes smoothness constraints on adjacent classifiers. We show that such patterns can be effectively learned in the dual form of the classical SVM, and further show that a parsimonious solution can be achieved in the primal form. Although a solution can be effectively optimized via gradient descent, the technical development is not straightforward, requiring a relaxation over the loss function of SVMs. We demonstrate the performance of our algorithm in two practical application domains: team performance and road traffic prediction. Empirical results show our model not only achieves competitive prediction accuracy, but its discovered patterns truly capture and give intuition about the variation in the data distribution across multiple data clusters.