In this work, we propose two novel quantum walk kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), between un-attributed graph structures. Different from most classical graph kernels, the proposed HAQJSK kernels can incorporate hierarchical aligned structure information between graphs and transform graphs of random sizes into fixed-size aligned graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of vertices and the Hierarchical Transitive Aligned Density Matrix of the Continuous-Time Quantum Walks (CTQW). With pairwise graphs to hand, the resulting HAQJSK kernels are defined by computing the Quantum Jensen-Shannon Divergence (QJSD) between their transitive aligned graph structures. We show that the proposed HAQJSK kernels not only reflect richer intrinsic whole graph characteristics in terms of the CTQW, but also address the drawback of neglecting structural correspondence information that arises in most R-convolution graph kernels. Moreover, unlike the previous QJSD based graph kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can simultaneously guarantee the properties of permutation invariant and positive definiteness, explaining the theoretical advantages of the HAQJSK kernels. The experiment indicates the effectiveness of the new proposed kernels.

In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.

Underwater images normally suffer from visual degradation issues such as color deviations, low contrasts, and blurred details. Recently, numerous underwater image enhancement algorithms have been proposed to address these issues. However, constrained by underwater conditions, acquiring nonunderwater images and depth maps for underwater images is often challenging. This limitation significantly hampers the performance of data-driven-based methods and physical model-based methods. In addition, existing physical model-based methods typically require manual parameter settings, which tend to be bruteforce and insufficient to effectively address the diverse underwater scenes. To overcome these limitations, this article presents a comprehensive underwater image enhancement framework comprising three phases: meta submergence (metamergence), meta relief (metalief), and meta ebb (metaebb). These phases are dedicated to virtual underwater image synthesis, underwater image depth map estimation, and the configuration of state-of-the-art physical models for underwater image enhancement by reinforcement learning, separately. While the three phases are trained separately, the former phase provides the necessary data for training the latter. We refer to the overall three phases as metalantis (i.e., meta Atlantis) because its training processes, involving variations from submergence via relief to ebb over indoor scenes, mimic the virtual variations of Atlantis. The metalantis framework empowers state-of-the-art physical models of underwater imaging through reinforcement learning with virtually generated data. The well-trained metalantis framework can take an underwater image as the sole input, process it into virtual representations, and finally enhance it. Comprehensive qualitative and quantitative empirical evaluations validate that our metalantis framework outperforms state-of-the-art underwater image enhancement methods. We release our code at https://gitee.com/wanghaoupc/Metalantis_UIE .

Hypergraph neural networks (HNNs) have shown promise in handling tasks characterized by high-order correlations, achieving notable success across various applications. However, there has been limited focus on heterophilic hypergraph learning (HHL), in contrast to the increasing attention given to graph neural networks designed for graphs exhibiting heterophily. This paper aims to pave the way for HHL by addressing key gaps from multiple perspectives: measurement, dataset diversity, and baseline model development. First, we introduce metrics to quantify heterophily in hypergraphs, providing a numerical basis for assessing the homophily/heterophily ratio. Second, we develop diverse benchmark datasets across various real-world scenarios, facilitating comprehensive evaluations of existing HNNs and advancing research in HHL. Additionally, as a novel baseline model, we propose HyperUFG, a framelet-based HNN integrating both low-pass and high-pass filters. Extensive experiments conducted on synthetic and benchmark datasets highlight the challenges current HNNs face with heterophilic hypergraphs, while showcasing that HyperUFG performs competitively and often outperforms many existing models in such scenarios. Overall, our study underscores the urgent need for further exploration and development in this emerging field, with the potential to inspire and guide future research in HHL.

Network representations are powerful tools to modeling the dynamic time-varying financial complex systems consisting of multiple co-evolving financial time series, e.g., stock prices. In this work, we develop a novel framework to compute the kernel-based similarity measure between dynamic time-varying financial networks. Specifically, we explore whether the proposed kernel can be employed to understand the structural evolution of the financial networks with time associated with standard kernel machines. For a set of time-varying financial networks with each vertex representing the individual time series of a different stock and each edge between a pair of time series representing the absolute value of their Pearson correlation, our start point is to compute the commute time (CT) matrix associated with the weighted adjacency matrix of the network structures, where each element of the matrix can be seen as the enhanced correlation value between pairwise stocks. For each network, we show how the CT matrix allows us to identify a reliable set of dominant correlated time series as well as an associated dominant probability distribution of the stock belonging to this set. Furthermore, we represent each original network as a discrete dominant Shannon entropy time series computed from the dominant probability distribution. With the dominant entropy time series for each pair of financial networks to hand, we develop an entropic dynamic time warping kernels through the classical dynamic time warping framework, for analyzing the financial time-varying networks. We show that the proposed kernel bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks extracted through New York Stock Exchange (NYSE) database demonstrate that the effectiveness of the proposed method.