To enhance the capability of Graph Neural Networks (GNNs) in judging graph isomorphism and graph classification tasks, this paper introduces a metric space-based graph isomorphism judgment method called the k-MSI test, which offers more topological information than the k-WL test and demonstrates superior graph isomorphism judgment capabilities compared to the k-WL test at the same complexity level. On the open test isomorphic dataset BREC, our k-MSI test accuracy rate is more than 11% ahead of the other methods. Furthermore, based on the k-MSI test, we propose a feature enhancement method Node Metric Indicator (NMI) that supplies additional topological information of graphs for GNNs and presents a novel GNN named Metric Space Indicators Graph Neural Network (MSIGNN). Experimental results on a publicly available benchmark graph classification task indicate that the NMI feature-based MSIGNN outperforms state-of-the-art methods on the BREC graph isomorphism test dataset and achieves satisfactory performance on real-world datasets.

Spatiotemporal kernel density visualization (STKDV) is used extensively for many geospatial analysis tasks, including traffic accident hotspot detection, crime hotspot detection, and disease outbreak detection. However, STKDV is a computationally expensive operation, which does not scale to large-scale datasets, high resolutions, and a large number of timestamps. Although a recent approach, the sliding-window-based solution (SWS), reduces the time complexity of STKDV, it (i) is unable to reduce the time complexity for supporting STKDV-based exploratory analysis, (ii) is not theoretically efficient, and (iii) does not provide optimization techniques for bandwidth tuning. To eliminate these drawbacks, we propose a prefix-set-based solution (PREFIX) that encompasses three methods, namely PREFIXsingle(addressing (i)), PREFIXmultiple(addressing (ii)), and PREFIXtuning(addressing (iii)). We offer theoretical and practical evidence that PREFIX is capable of outperforming the state-of-the-art solution (SWS). In particular, PREFIX achieves at least 115x to 1,906x speedups and is the first solution that can efficiently generate multiple high-resolution STKDVs for the large-scale New York taxi dataset with 13.6 million data points.

Despite the theoretical expressiveness of 2-dimensional Folklore Weisfeiler-Lehman (2-FWL) Graph Neural Networks (GNNs), a significant gap persists between their theoretical capacity and their practical performance. To bridge this gap, we identify a critical limitation in current Graph Structural Encodings (GSEs): insufficient sensitivity to subtle structural variations, particularly in local connectivity, spectral features, and distance-based patterns. We show that widely used GSEs-such as Relative Random Walk Probability (RRWP) and monomial-based methods-lack full sensitivity across spectral frequency bands and long-range distances. Moreover, they fail to capture fine-grained local connectivity, which is essential for identifying cut nodes, biconnected components, and other higher-order structures that 2-FWL GNNs theoretically encode. To address these limitations, we propose CSDGSE (Connectivity, Spectral, and Distance Graph Structural Encoding), a novel GSE framework that jointly enhances sensitivity to: (1) exact local connectivity via hierarchical graph decomposition(2) full-frequency spectral features using expressive graph polynomials (e.g., Chebyshev), and (3) full-range distance interactions. A key innovation is our scalable divide-and-conquer algorithm for computing exact local connectivity across all node pairs, enabling efficient integration into modern GSEs. Extensive experiments show that CSDGSE outperforms existing GSEs in capturing complex structural patterns, achieving state-of-the-art results on molecular property prediction benchmarks like ZINC. Our work sets a new standard for GSEs by aligning theoretical expressiveness with practical effectiveness through enhanced structural sensitivity.

Existing message passing-based and transformer-based graph neural networks (GNNs) cannot satisfy requirements for learning representative graph embeddings due to restricted receptive fields, redundant message passing, and reliance on fixed aggregations. These methods face scalability and expressivity limitations from intractable exponential growth or quadratic complexity, restricting interaction ranges and information coverage across large graphs. Motivated by the analysis of long-range graph structures, we introduce a novel Graph Neural Network called Hub-Fringe Graph Neural Network (HFGNN). Our Hub-Fringe structure, drawing inspiration from the graph indexing technique known as Hub Labeling, offers a straightforward and effective approach for learning scalable graph representations while ensuring comprehensive coverage of information. HFGNN leverages this structure to enable selective propagation of relevant embeddings through a carefully designed message function. Theoretical analysis is presented to show the expressivity and scalability of the proposed method. Empirically, HFGNN exceeds standard GNNs on tasks including classification and regression, especially for large, long-range graphs where scalability and coverage matter. Ablation studies further confirm the benefits of our hub-fringe based graph neural network, including improved expressivity and scalability. The source codes is available at https://github.com/nick12340/HFGNN.

Kernel density visualization (KDV) has been widely used in many geospatial analysis tasks, including traffic accident hotspot detection, crime hotspot detection, and disease outbreak detection. Although KDV can be supported by many scientific, geographical, and visualization software tools, none of these tools can support high-resolution KDV with large-scale datasets. Therefore, we develop the first versatile programming library, called LIBKDV, based on the set of our complexity-optimized algorithms. Given the high efficiency of these algorithms, LIBKDV not only accelerates the KDV computation but also enriches KDV-based geospatial analytics, including bandwidth-tuning analysis and spatiotemporal analysis, which cannot be natively and feasibly supported by existing software tools. In this demonstration, participants will be invited to use our programming library to explore interesting hotspot patterns on large-scale traffic accident, crime, and COVID-19 datasets.

Kernel density visualization (KDV) has been the de facto method in many spatial analysis tasks, including ecological modeling, crime hotspot detection, traffic accident hotspot detection, and disease outbreak detection. In these tasks, domain experts usually generate multiple KDVs with different bandwidth values. However, generating a single KDV, let alone multiple KDVs, is time-consuming. In this paper, we develop a share-and-aggregate framework, namely SAFE, to reduce the time complexity of generating multiple KDVs given a set of bandwidth values. On the other hand, domain experts can specify bandwidth values on the fly. To tackle this issue, we further extend SAFE and develop the exact method SAFE all and the 2-approximation method SAFE exp which reduce the time complexity under this setting. Experimental results on four large-scale datasets (up to 4.33M data points) show that these three methods achieve at least one-order-of-magnitude speedup for generating multiple KDVs in most of the cases without degrading the visualization quality.

Spatial-temporal kernel density visualization (STKDV) has been extensively used in a wide range of applications, e.g., disease outbreak analysis, traffic accident hotspot detection, and crime hotspot detection. While STKDV can provide accurate and comprehensive data visualization, computing STKDV is time-consuming, which is not scalable to large-scale datasets. To address this issue, we develop a new sliding-window-based solution (SWS), which theoretically reduces the time complexity for generating STKDV, without increasing the space complexity. Moreover, we incorporate SWS with the progressive visualization framework, which can continuously output partial visualization results to users (from coarse to fine), until users satisfy the visualization. Our experimental studies on five large-scale datasets show that SWS achieves 1.71x to 24x speedup compared with the state-of-the-art methods.

Kernel density visualization (KDV) is a commonly used visualization tool for many spatial analysis tasks, including disease outbreak detection, crime hotspot detection, and traffic accident hotspot detection. Although the most popular geographical information systems, e.g., QGIS, and ArcGIS, can also support this operation, these solutions are not scalable to generate a single KDV for datasets with million-scale data points, let alone to support exploratory operations (e.g., zoom in, zoom out, and panning operations) with KDV in near real-time (< 5 sec). In this demonstration, we develop a near real-time visualization system, called KDV-Explorer, that is built on top of our prior study on the efficient kernel density computation. Participants will be invited to conduct some kernel density analysis on three large-scale datasets (up to 1.3 million data points), including the traffic accident dataset, crime dataset and COVID-19 dataset. We will also compare the performance of our solution and the solutions in QGIS and ArcGIS.