Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the underlying relation between entities is pre-determined. However, the explicit graph structure (relation) does not necessarily reflect the true dependency and genuine relation may be missing due to the incomplete connections in the data. Furthermore, existing methods are ineffective to capture the temporal trends as the RNNs or CNNs employed in these methods cannot capture long-range temporal sequences. To overcome these limitations, we propose in this paper a novel graph neural network architecture, {Graph WaveNet}, for spatial-temporal graph modeling. By developing a novel adaptive dependency matrix and learn it through node embedding, our model can precisely capture the hidden spatial dependency in the data. With a stacked dilated 1D convolution component whose receptive field grows exponentially as the number of layers increases, Graph WaveNet is able to handle very long sequences. These two components are integrated seamlessly in a unified framework and the whole framework is learned in an end-to-end manner. Experimental results on two public traffic network datasets, METR-LA and PEMS-BAY, demonstrate the superior performance of our algorithm.

Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics. Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data, but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in real-world graph data. In this paper, we propose a novel adversarial graph embedding framework for graph data. The framework encodes the topological structure and node content in a graph to a compact representation, on which a decoder is trained to reconstruct the graph structure. Furthermore, the latent representation is enforced to match a prior distribution via an adversarial training scheme. To learn a robust embedding, two variants of adversarial approaches, adversarially regularized graph autoencoder (ARGA) and adversarially regularized variational graph autoencoder (ARVGA), are developed. Experimental studies on real-world graphs validate our design and demonstrate that our algorithms outperform baselines by a wide margin in link prediction, graph clustering, and graph visualization tasks.

Graph clustering is a fundamental task which discovers communities or groups in networks. Recent studies have mostly focused on developing deep learning approaches to learn a compact graph embedding, upon which classic clustering methods like k-means or spectral clustering algorithms are applied. These two-step frameworks are difficult to manipulate and usually lead to suboptimal performance, mainly because the graph embedding is not goal-directed, i.e., designed for the specific clustering task. In this paper, we propose a goal-directed deep learning approach, Deep Attentional Embedded Graph Clustering (DAEGC for short). Our method focuses on attributed graphs to sufficiently explore the two sides of information in graphs. By employing an attention network to capture the importance of the neighboring nodes to a target node, our DAEGC algorithm encodes the topological structure and node content in a graph to a compact representation, on which an inner product decoder is trained to reconstruct the graph structure. Furthermore, soft labels from the graph embedding itself are generated to supervise a self-training graph clustering process, which iteratively refines the clustering results. The self-training process is jointly learned and optimized with the graph embedding in a unified framework, to mutually benefit both components. Experimental results compared with state-of-the-art algorithms demonstrate the superiority of our method.

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph-analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the reconstruction errors for graph data. They have mostly overlooked the embedding distribution of the latent codes, which unfortunately may lead to inferior representation in many cases. In this article, we present a novel adversarially regularized framework for graph embedding. By employing the graph convolutional network as an encoder, our framework embeds the topological information and node content into a vector representation, from which a graph decoder is further built to reconstruct the input graph. The adversarial training principle is applied to enforce our latent codes to match a prior Gaussian or uniform distribution. Based on this framework, we derive two variants of the adversarial models, the adversarially regularized graph autoencoder (ARGA) and its variational version, and adversarially regularized variational graph autoencoder (ARVGA), to learn the graph embedding effectively. We also exploit other potential variations of ARGA and ARVGA to get a deeper understanding of our designs. Experimental results that compared 12 algorithms for link prediction and 20 algorithms for graph clustering validate our solutions.

Personalized decision-making can be implemented in a Federated learning (FL) framework that can collaboratively train a decision model by extracting knowledge across intelligent clients, e.g. smartphones or enterprises. FL can mitigate the data privacy risk of collaborative training since it merely collects local gradients from users without access to their data. However, FL is fragile in the presence of statistical heterogeneity that is commonly encountered in personalized decision making, e.g., non-IID data over different clients. Existing FL approaches usually update a single global model to capture the shared knowledge of all users by aggregating their gradients, regardless of the discrepancy between their data distributions. By comparison, a mixture of multiple global models could capture the heterogeneity across various clients if assigning the client to different global models (i.e., centers) in FL. To this end, we propose a novel multi-center aggregation mechanism to cluster clients using their models’ parameters. It learns multiple global models from data as the cluster centers, and simultaneously derives the optimal matching between users and centers. We then formulate it as an optimization problem that can be efficiently solved by a stochastic expectation maximization (EM) algorithm. Experiments on multiple benchmark datasets of FL show that our method outperforms several popular baseline methods. The experimental source codes are publicly available on the Github repository (GitHub repository: https://github.com/mingxuts/multi-center-fed-learning).