Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriad graph analytic tasks and applications. Most GNNs rely on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GNNs for heterophilic graphs</i> are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that governs existing heterophilic GNN models, along with general summaries and detailed analyses. Furthermore, we discuss the relationship between heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out potential directions to advance and inspire future research and applications on heterophilic graph learning with GNNs.

This paper proposes a family of Aligned Entropic Graph Kernels (AEGK) for graph classification, based on the Averaged Mixing Matrix (AMM) of Continuous-time Quantum Walks (CTQWs). Specifically, we show how the AMM matrix allows us to compute a quantum Shannon entropy of each vertex for either un-attributed or attributed graphs. For pairwise graphs, the proposed AEGK kernels are defined by computing the kernel-based similarity between the quantum Shannon entropies of their pairwise aligned vertices. Theoretical analysis reveals that the AEGK kernels can not only integrate the structural correspondence information between graphs, but also discriminate the structural differences between aligned vertices. Moreover, the AEGK kernels can simultaneously capture both global and local structural characteristics through the quantum Shannon entropies. These theoretical properties explain the effectiveness.

This paper proposes a family of Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK) for un-attributed graphs. The HAQJSK kernels can incorporate hierarchical correspondence information between graphs, and thus transform arbitrary sized graphs into fix-sized aligned structures, i.e., the hierarchical transitive aligned Adjacency Matrix of vertices or Density Matrix of Continuous-Time Quantum Walks (CTQWs). For pairwise graphs, the resulting HAQJSK kernels are defined by computing the Quantum Jensen-Shannon Divergence (QJSD) between their aligned structures. Unlike classical graph kernels, the HAQJSK kernels can either reflect global intrinsic structure characteristics through CTQWs, or address the drawback of neglecting structural correspondence information, theoretically explaining the effectiveness.

In this work, we develop a family of Aligned Entropic Graph Kernels (AEGK) for graph classification. We commence by performing the Continuous-time Quantum Walk (CTQW) on each graph structure, and compute the Averaged Mixing Matrix (AMM) to describe how the CTQW visits all vertices from a starting vertex. More specifically, we show how this AMM matrix allows us to compute a quantum Shannon entropy of each vertex for either un-attributed or attributed graphs. For pairwise graphs, the proposed AEGK kernels are defined by computing the kernel-based similarity between the quantum Shannon entropies of their pairwise aligned vertices. The analysis of theoretical properties reveals that the proposed AEGK kernels cannot only address the shortcoming of neglecting the structural correspondence information between graphs arising in most existing R-convolution graph kernels, but also overcome the problems of neglecting the structural differences and vertex-attributed information arising in existing vertex-based matching kernels. Moreover, unlike most existing classical graph kernels that only focus on the global or local structural information of graphs, the proposed AEGK kernels can simultaneously capture both global and local structural characteristics through the quantum Shannon entropies, reflecting more precise kernel-based similarity measures between pairwise graphs. The above theoretical properties explain the effectiveness of the proposed AEGK kernels. Experimental evaluations demonstrate that the proposed kernels can outperform state-of-the-art graph kernels and deep learning models for graph classification.

Electric bicycles (EBs) have gained immense popularity as an environmentally friendly and convenient transportation mode. However, range anxiety remains a major concern for EB users. This paper presents a real-time route planning model focused on predicting the remaining range of EBs. First, we represent the user's interaction data and the real-time battery state as a dynamic graph. Then we propose a novel approach called the Real-Time Electric Bicycle Remaining Range (RtRR) prediction model, which leverages the graph structure and jointly optimizes temporal edge convolution, LSTM, and Transformer models to estimate the remaining EB battery range. Based on the prediction, we can update the optimal cycling routes for users in real-time, considering charging station locations. Extensive evaluations demonstrate that our proposed RtRR model outperforms 9 baseline methods on real-world datasets. The route planning based on RtRR prediction effectively alleviates range anxiety and enhances the user experience. It can be accessed at https://github.com/gu-yongchun/Real-time-E-bike-Route-Planning-with-Battery-Range-Prediction.

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.

Deep learning (DL) based knowledge tracing (KT) models have challenges for uninterpretable prediction and parameter representation in educational applications, though they achieved remarkable outcomes in predicting the exercise performance of students. This paper proposes a novel knowledge tracing model of high precision and interpretability (namedXKT) for questions with multiple knowledge concepts based on cognitive learning theories and multidimensional item response theory (MIRT). TheXKTconsists of three differentiable network components: multi-feature embedding, cognition processing network, andMIRT-based neural predictor, which aim to provide an explainable prediction of student exercise performance. Specifically, inXKT, multi-feature embedding learns the rich semantic representation (e.g., knowledge distribution information) to enhance knowledge tracing using a cognition processing network. The cognition processing network performs selective perception, ability memory processing, and long-term knowledge memory processing to ensure the explainable factor representation for theMIRT-based neural predictor. Lastly, theMIRT-based neural predictor employs psychometric parameters to interpret student exercise predictions better. Extensive experiments on four real-world datasets show thatXKToutperforms existingKTmethods in predicting future learner responses. Moreover, ablation studies further show thatXKToffers good interpretability of student performance predictions with multiple knowledge concepts, indicating excellent potential in real-world educational applications.

To ease the process of building Knowledge Graphs (KGs) from scratch, a cost-effective method is required to enrich a KG using the triples extracted from a corpus. However, it is challenging to enrich a KG with newly extracted triples since they contain noisy information. This paper proposes to refine a KG by leveraging information extracted from a corpus. In particular, we first formulate the task of building KGs as two coupled sub-tasks, namely join event extraction and knowledge graph fusion. We then propose a collaborative knowledge graph fusion framework, which is composed of an explorer and a supervisor, to allow the involved two sub-tasks to mutually assist each other in an alternative manner. More concretely, an explorer extracts triples from a corpus supervised by both the ground-truth annotation and the KG provided by the supervisor. Furthermore, a supervisor then evaluates the extracted triples and enriches the KG with those that are highly ranked. To implement this evaluation, we further propose a translated relation alignment scoring mechanism to align and translate the extracted triples to the KG. Experimental results verify that this collaboration can improve both the performance of our sub-tasks, and contribute to high-quality enriched knowledge graphs.