Voronoi diagram is commonly used to visualize geographical point dataset with a collection of plane-partitioned facets. As the size of the geographical point dataset increases, facets are densely distributed, and present different sizes and irregular shapes, leading to overdrawing and confusion problems, and hampering the visual perception of Voronoi diagram and insightful exploration of geographical point data. In this paper, we propose a novel Voronoi diagram generation framework to visualize and explore large-scale geographical point datasets. Firstly, an attribute-based blue noise sampling model is designed to select a subset of points to generate the simplified Voronoi diagram, retaining both the spatial distribution and attribute relationship of the original large-scale geographical points. Then a couple of optimization schemes are integrated into the sampling model to replace the representative points, aiming to enhance the visual perception of Voronoi diagram, such as shape balance and color characterization. Furthermore, we implement an interactive online Voronoi diagram generation tool, GeoVoronoi, enabling users to generate meaningful facets according to their requirements. Quantitative comparisons, case studies and user studies based on real-world datasets have demonstrated the effectiveness of our proposed method in the generation of credible Voronoi diagram and in-depth exploration of geographical point datasets.

Chart images, such as bar charts, pie charts, and line charts, are explosively produced due to the wide usage of data visualizations. Accordingly, knowledge mining from chart images is becoming increasingly important, which can benefit downstream tasks like chart retrieval and knowledge graph completion. However, existing methods for chart knowledge mining mainly focus on converting chart images into raw data and often ignore their visual encodings and semantic meanings, which can result in information loss for many downstream tasks. In this paper, we propose ChartKG, a novel knowledge graph (KG) based representation for chart images, which can model the visual elements in a chart image and semantic relations among them including visual encodings and visual insights in a unified manner. Further, we develop a general framework to convert chart images to the proposed KG-based representation. It integrates a series of image processing techniques to identify visual elements and relations, e.g., CNNs to classify charts, yolov5 and optical character recognition to parse charts, and rule-based methods to construct graphs. We present four cases to illustrate how our knowledge-graph-based representation can model the detailed visual elements and semantic relations in charts, and further demonstrate how our approach can benefit downstream applications such as semantic-aware chart retrieval and chart question answering. We also conduct quantitative evaluations to assess the two fundamental building blocks of our chart-to-KG framework, i.e., object recognition and optical character recognition. The results provide support for the usefulness and effectiveness of ChartKG.

Numerous graph clustering methods have been proposed to explore aggregation structures across multiple graphs. In these methods, single-graph features are merely considered or multigraph features are simply weighted, which are insufficient for the construction of reasonable multiple graph clustering features, since the association information between pairwise graphs is ignored and the varied local correlations might influence the clustering preference. Thus, we propose an interactive multiple graph clustering model, iMGC, in this article, to achieve reasonable multiple graph clustering features, which cannot only express multiple relationships, but also preserve associations of nodes across multiple graphs. First, a unified graph matrix is constructed with the combination of structural differences quantified by graph representation learning, which is further optimized by minimizing the difference of structural characteristics between it and each single graph matrix. Thus, multiple relationships are well integrated and expressed, while the varied local correlations within different graphs are also balanced in the unified graph matrix. Then, a constrained Laplacian rank is applied on the unified graph matrix to generate the unified clustering result directly, which is able to preserve association features across multiple graphs. Furthermore, we provide a set of visualization and interaction interfaces, enabling users to intuitively optimize and evaluate the multiple graph clustering features, and interactively explore the multiple graphs. Case studies and quantitative comparisons based on real-world datasets have demonstrated the effectiveness of iMGC in the clustering performance from various perspectives and exploration of multiple graphs.

Numerous sampling strategies have been proposed to simplify large-scale networks for highly readable visualizations. It is of great challenge to preserve contextual structures formed by nodes and edges with tight relationships in a sampled graph, because they are easily overlooked during the process of sampling due to their irregular distribution and immunity to scale. In this paper, a new graph sampling method is proposed oriented to the preservation of contextual structures. We first utilize a graph representation learning (GRL) model to transform nodes into vectors so that the contextual structures in a network can be effectively extracted and organized. Then, we propose a multi-objective blue noise sampling model to select a subset of nodes in the vectorized space to preserve contextual structures with the retention of relative data and cluster densities in addition to those features of significance, such as bridging nodes and graph connections. We also design a set of visual interfaces enabling users to interactively conduct context-aware sampling, visually compare results with various sampling strategies, and deeply explore large networks. Case studies and quantitative comparisons based on real-world datasets have demonstrated the effectiveness of our method in the abstraction and exploration of large networks.

Geographical areal data usually presents hierarchical structures, and its characteristics vary at different scales. At the higher scales, the visualization of geographical areal data is abstract and the detailed features are easily missed. As a difference, more detailed information is presented at the lower scales while the visual perception of global features is easily disturbed due to the overdrawing of visual elements. As the geographical areal data is visualized at a single scale at the same time, it seems impossible to balance the visual perception of both the global features and detailed characteristics. In this paper, we propose a multi-scale geographical areal data visualization method based on spatial attribute association to enhance the visual perception of both the global features and detailed characteristics. Firstly, the geographical areal data is aggregated into hierarchical clusters based on the spatial similarity. Then, the coefficient of variation is applied to estimate the attribute distribution of each cluster in the hierarchy, and a novel geographical areal data visualization scheme is proposed to adaptively present the multi-scale clusters with lower variation coefficients at the same time. In addition, a rich set of visual interfaces and user-friendly interactions are provided enabling users to specify those clusters of interest at different scales and compare multi-scale visualizations with different hierarchies. Finally, we implement a geographical areal data visualization framework, allowing users to visually explore the global features and detailed characteristics at the same time and get deeper insights into the potential features in the geographical areal data. Case studies and quantitative comparisons based on real-world datasets have been conducted to demonstrate the effectiveness of the proposed multi-scale visualization method for in-depth visual exploration of geographical areal data.