Learning representation of the enclosing subgraph of node pairs is recognized as an efficient approach for link-oriented prediction tasks in network applications. The core challenge within this subgraph encoding approach is how to effectively distinguish and then properly aggregate the contribution of nodes in the subgraph into a single vector to indicate the relation between the target node pair. In this work, we propose a novel sphere-based subgraph encoding architecture, namely BS-SubGNN, to address the challenge. In detail, we design two key building blocks, including Bicentric Sphere Node Labeling (BSNL) and Bicentric Sphere Subgraph Pooling (BSSP) to assist message passing in BS-SubGNN. BSNL endows each node a label according to the sphere it belongs to in the subgraph to distinguish the contribution of nodes, while BSSP adopts an attention mechanism to aggregate the contribution of nodes in each sphere. Theoretically, we prove that BS-SubGNN can unify existing node distance labeling methods, and yield discriminative node features with less time complexity. We evaluate the performance of BS-SubGNN in link prediction tasks over a variety of network types, including undirected networks, attribute networks, directed networks, and signed directed networks. Our experimental results demonstrate that BS-SubGNN consistently achieves significant performance improvements over the above diverse types of networks. In particular, compared to those methods with a requisite of multi-hop neighborhood information, BS-SubGNN can obtain better performance even when only one-hop neighborhood information of the node pair is utilized.

In this article, we consider the problem of inferring the sign of a link based on known sign data in signed networks. Regarding this link sign prediction problem, signed directed graph neural networks (SDGNNs) provides the best prediction performance currently to the best of our knowledge. In this article, we propose a different link sign prediction architecture called subgraph encoding via linear optimization (SELO), which obtains overall leading prediction performances compared to the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization (LO) method. Comprehensive experiments are conducted on five real-world signed networks with area under curve (AUC), F1, micro-F1, and macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the five real-world networks and in all the four evaluation metrics.

In this article, we consider the problem of distributed game-theoretic learning in games with finite action sets. A timestamp-based inertial best-response dynamics is proposed for Nash equilibrium seeking by players over a communication network. We prove that if all players adhere to the dynamics, then the states of players will almost surely reach consensus and the joint action profile of players will be absorbed into a Nash equilibrium of the game. This convergence result is proven under the condition of weakly acyclic games and strongly connected networks. Furthermore, to encounter more general circumstances, such as games with graphical action sets, state-based games, and switching communication networks, several variants of the proposed dynamics and its convergent results are also developed. To demonstrate the validity and applicability, we apply the proposed timestamp-based learning dynamics to design distributed algorithms for solving some typical finite games, including the coordination games and congestion games.

In this article, an augmented game approach is proposed for the formulation and analysis of distributed learning dynamics in multiagent games. Through the design of the augmented game, the coupling structure of utility functions among all the players can be reformulated into an arbitrary undirected connected network while the Nash equilibria are preserved. In this case, any full-information game learning dynamics can be recast into a distributed form, and its convergence can be determined from the structure of the augmented game. We apply the proposed approach to generate both deterministic and stochastic distributed gradient play and obtain several negative convergent results about the distributed gradient play: 1) a Nash equilibrium is convergent under the classic gradient play, yet its corresponding augmented Nash equilibrium may be not convergent under the distributed gradient play and, on the other side, 2) a Nash equilibrium is not convergent under the classic gradient play, yet its corresponding augmented Nash equilibrium may be convergent under the distributed gradient play. In particular, we show that the variational stability structure (including monotonicity as a special case) of a game is not guaranteed to be preserved in its augmented game. These results provide a systematic methodology about how to formulate and then analyze the feasibility of distributed game learning dynamics.

The enclosing subgraph of a target link has been proved to be effective for prediction of potential links. However, it is still unclear what topological features of the subgraph play the key role in determining the existence of links. To give a possible answer to this question, in this paper, we propose a neural network based learning method for link prediction with only 1-hop neighborhood information. In detail, we extract the one-hop neighborhood of a target link as the enclosing subgraph, then encode the subgraph into different types of topological features, and lastly feed these features to train a fully connected neural network for link prediction. The experimental results show that our proposed learning method with the 1-hop neighborhood features could outperform those heuristic-based methods and achieve nearly equal performance to the state-of-the-art learning-based method WLNM and SEAL. Furthermore, it is observed that these features can be concatenated with attribute vectors to greatly promote the link prediction performance in attributed graphs. This indicates that the topological pattern within an enclosing subgraph, which determines the existence of a possible link, can be aggregated by some elementary subgraph features.

In this article, a consensus-based multipopulation game dynamics approach is proposed for distributed Nash equilibria seeking and optimization. The approach is fundamentally different from existing population dynamics from that: 1) the underlying communication network underlying the population game dynamics could be arbitrary undirected connected graph and more importantly 2) the proposed approach works in a distributed manner even when the objective functions of players are strongly coupled with each other. The proposed approach greatly extends the applicability of population game dynamics in distributed optimization and learning problems. A distributed constrained optimization problem and a traffic routing problem are utilized to illustrate the feasibility of the proposed multipopulation game dynamics approach.

Face illumination transfer from a single image is still a challenging problem. Most current methods fail when the reference face and the target face differ obviously in pose or facial geometry. In this paper, we propose a face illumination transfer method based on eye-relit 3D basis to conquer this problem. We extract the environment map from one eye of the reference image, preventing the illumination misestimation caused by the reference's pose and facial geometry. By relighting our 3D basis with the map, our transfer result preserves the illumination of the reference image, and the pose and geometry of the target image. Experiments demonstrate our method's good performance in above-mentioned challenging cases.

ABSTRACT This paper proposes a novel video‐based method to transfer the illumination from a single reference facial performance video to a target one taken under nearly uniform illumination. We first filter the key frames of the reference and the target face videos with an edge‐preserving filter. Then, the illumination component of reference key frame is extracted through dividing the filtered reference key frames by the corresponding filtered target key frames in skin region. The differences in non‐skin region caused by different expressions between the reference and target face may bring about artifacts. Therefore, we interpolate the illumination component of the non‐skin region by that of the surrounded skin region to ensure the spatial smoothness and consistency. After that, the illumination components of key frames are propagated to non‐key frames to ensure the temporal consistency between the two adjacent frames. We obtain convincing results by transferring the illumination effects of a single reference facial performance video to a target one with the spatial and temporal consistencies preserved. Copyright © 2013 John Wiley & Sons, Ltd.

Successful processing of Synthetic Aperture Radar (SAR) requires that the Doppler centroid frequency (f/sub dc/) be accurately estimated. The energy balancing method is one of the methods to estimate the f/sub dc/, though it has some shortcomings. The paper brings forward an improved method which estimates the f/sub dc/ more effectively. This paper finally shows the new method's results by processing raw data and analyzes its performance. A conclusion is drawn that the results of the improved method are precise; furthermore, the improved method can compute the f/sub dc/ without iterative computations, so it is more suitable for real time processing on DSP and has higher efficiency.