Heterophily has been considered as an issue that hurts the performance of Graph Neural Networks (GNNs). To address this issue, some existing work uses a graph-level weighted fusion of the information of multi-hop neighbors to include more nodes with homophily. However, the heterophily might differ among nodes, which requires to consider the local topology. Motivated by it, we propose to use the local similarity (LocalSim) to learn node-level weighted fusion, which can also serve as a plug-and-play module. For better fusion, we propose a novel and efficient Initial Residual Difference Connection (IRDC) to extract more informative multi-hop information. Moreover, we provide theoretical analysis on the effectiveness of LocalSim representing node homophily on synthetic graphs. Extensive evaluations over real benchmark datasets show that our proposed method, namely Local Similarity Graph Neural Network (LSGNN), can offer comparable or superior state-of-the-art performance on both homophilic and heterophilic graphs. Meanwhile, the plug-and-play model can significantly boost the performance of existing GNNs.

Maritime trajectory modeling is crucial for ensuring the safety and efficiency of maritime transportation. However, the unique challenges of the open ocean—such as the lack of a pre-determined road network and infrequent vessel interactions—render traditional land-based route prediction systems inadequate. To overcome these obstacles, we present ST-Shape, a spatio-temporal trajectory indexing method designed to swiftly retrieve pertinent historical maritime trajectories, thereby facilitating long-term trajectory prediction. ST-Shape approximates trajectories using two-dimensional polygons and constructs the index with shape indices, thus preserving the spatio-temporal properties of each trajectory. Concurrently, we introduce a straightforward yet robust model that harnesses this indexed data to predict vessel movements. To underpin our research, we have curated a comprehensive maritime trajectory dataset from the Atlantic and Pacific Oceans, classified according to diverse navigational scenarios. Our endeavor serves as a foundational step towards expedited spatio-temporal trajectory retrieval for maritime trajectory prediction, marking a significant stride in enhancing maritime safety and navigational efficiency.

Incomplete node features are ubiquitous in real-world scenarios such as user profiling and cold-start recommendation, which severely hinders the practical deployment of graph learning systems (e.g., GNNs). Existing solutions typically rely on diffusion-based structural smoothing (e.g., feature propagation) to impute missing values. However, we find that these approaches suffer from structural overfitting, leading to three progressive challenges: 1) performance degradation on disjoint graphs, 2) loss of semantic diversity due to over-smoothing, and 3) feature distribution shift when generalizing to unseen graph structures (inductive tasks). To address these challenges, we introduce the DART framework. It begins by employing Global Structural Augmentation (GSA), which establishes global correlations to bridge disjoint components and extend diffusion coverage. Building upon this, we design a semantic rectifier based on masked autoencoding. This module learns the latent feature manifold to recover natural semantic details. Crucially, we introduce a test-time distribution rectification mechanism that projects structurally biased features back onto the learned manifold during inference, effectively bridging the inductive distribution gap. Furthermore, considering that synthetic masking fails to reflect realworld sparsity, we present a new dataset Sailing collected from voyage records with naturally missing attributes. Extensive experiments on six public datasets and Sailing demonstrate that DART significantly outperforms state-of-the-art methods in both transductive and inductive settings. Our code and dataset are available at https://github.com/yfsong00/DART.