Retrieval-Augmented Generation (RAG) has significantly enhanced Large Language Models' ability to access external knowledge, yet current graph-based RAG approaches face two critical limitations in managing hierarchical information: they impose rigid layer-specific compression quotas that damage local graph structures, and they prioritize topological structure while neglecting semantic content. We introduce T-Retriever, a novel framework that reformulates attributed graph retrieval as tree-based retrieval using a semantic and structure-guided encoding tree. Our approach features two key innovations: (1) Adaptive Compression Encoding, which replaces artificial compression quotas with a global optimization strategy that preserves the graph's natural hierarchical organization, and (2) Semantic-Structural Entropy (S²-Entropy), which jointly optimizes for both structural cohesion and semantic consistency when creating hierarchical partitions. Experiments across diverse graph reasoning benchmarks demonstrate that T-Retriever significantly outperforms state-of-the-art RAG methods, providing more coherent and contextually relevant responses to complex queries.

Large-scale color datasets exhibit significant sparsity in name-color correspondences, substantially impeding the effectiveness of conventional methodologies. We propose a contrastive learning-based framework for color name generation and recommendation that addresses sparsity through negative sampling, supporting two core tasks: color-to-name recommendation and name-to-color generation. Our framework employs a multi-task contrastive learning architecture comprising three key components: (1) a pre-trained Transformer-based name encoder, (2) an RGB encoder, and (3) an RGB generator. The framework utilizes negative sampling to construct positive-negative pairs, contrasting RGB encoder outputs with positive and negative name embeddings. We adopt a multi-objective optimization strategy incorporating binary cross-entropy loss for neural collaborative filtering, and mean squared error loss for name-to-RGB mapping. Experimental results demonstrate substantial improvements over baseline methods, achieving 71.26% Top-10 accuracy in color-to-name recommendation and reducing CIELAB distance error to 26.61 in name-to-color generation.

SUMMARY: Cryo-electron microscopy (cryo-EM) visualization transforms high-resolution 3D density volumes into intuitive representations, playing a vital role in structural biology. However, the increasing scale of cryo-EM data poses challenges for interactive visualization, including storage, transmission, and exploration. To address this, we propose a hybrid quantized implicit neural representation (INR) method that compresses cryo-EM volumes while supporting efficient on-demand access. To evaluate its effectiveness, we benchmark our approach against traditional compression techniques and one classic INR compressor, assessing both compression efficiency and visual quality. Beyond standard metrics, we examine performance on key cryo-EM tasks, including overall structure identification, secondary structure recognition, and fine-chain inspection. Our results demonstrate that the quantized INR achieves superior storage efficiency and task-relevant fidelity, and we provide an interactive tool and guidelines to assist users in selecting optimal compression strategies. AVAILABILITY: To facilitate future research, we provide our quantized neural representation approach and interactive tool available at Zenodo (https://doi.org/10.5281/zenodo.19688284) and GitHub (https://github.com/ChiefMoo/Lossy-Cryo-EM-Compression).

Bioscientists frequently seek to visualize the biological systems they have empirically characterized and reported in the literature. Realizing such visualizations requires biological structure modeling, an inherently complex process that demands both biological and geometric understanding. This paper addresses the problem of constructing such 3D models for visualization. In this paper, we introduce a novel agent framework that mitigates the challenges of operating 3D modeling software by transforming user inputs, including natural language descriptions, research publication content, and textual descriptions of the existing objects and structures in the current scene, into modeling operations in a structured JSON format and final 3D results. The major technical contribution lies in the collaborative agent design that simultaneously supports model planning, execution, and novel user interaction design, such as interactive modeling execution and dynamic widget generation that fuse text and mouse interaction within the chat window. The framework further incorporates a customized modeling memory to enhance user interaction, featuring components such as personalized memory management, feedback collection, and skill library design. This modeling memory is leveraged to enable improved 3D modeling performance over time. The quantitative evaluation on our collected dataset showcases the effectiveness of our framework. We also develop a prototype tool, Chat Modeling, and demonstrate its usage through two modeling case studies. Our user study and expert interviews highlight the potential of our approach for use in scientific workflows.

Recovering a continuous colormap from a single 2D scalar field visualization can be quite challenging, especially in the absence of a corresponding color legend. In this paper, we propose a novel colormap recovery approach that extracts the colormap from a color-encoded 2D scalar field visualization by simultaneously predicting the colormap and underlying data using a decoupling-and-reconstruction strategy. Our approach first separates the input visualization into colormap and data using a decoupling module, then reconstructs the visualization with a differentiable color-mapping module. To guide this process, we design a reconstruction loss between the input and reconstructed visualizations, which serves both as a constraint to ensure strong correlation between colormap and data during training, and as a self-supervised optimizer for fine-tuning the predicted colormap of unseen visualizations during inferencing. To ensure smoothness and correct color ordering in the extracted colormap, we introduce a compact colormap representation using cubic B-spline curves and an associated color order loss. We evaluate our method quantitatively and qualitatively on a synthetic dataset and a collection of real-world visualizations from the VIS30K dataset [9]. Additionally, we demonstrate its utility in two prototype applications-colormap adjustment and colormap transfer-and explore its generalization to visualizations with color legends and ones encoded using discrete color palettes.

Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples include geographical attributes like shared borders between countries or contextualized semantic information such as embedding vectors derived from large language models. In this work, we introduce a Voronoi treemap algorithm that leverages data similarity to generate neighborhood-preserving treemaps. First, we extend the treemap layout pipeline to consider similarity during data preprocessing. We then use a Kuhn-Munkres matching of similarities to centroidal Voronoi tessellation (CVT) cells to create initial Voronoi diagrams with equal cell sizes for each level. Greedy swapping is used to improve the neighborhoods of cells to match the data's similarity further. During optimization, cell areas are iteratively adjusted to their respective sizes while preserving the existing neighborhoods. We demonstrate the practicality of our approach through multiple real-world examples drawn from infographics and linguistics. To quantitatively assess the resulting treemaps, we employ treemap metrics and measure neighborhood preservation.

We present PiCCL (Pictorial Chart Composition Language), a new language that enables users to easily create pictorial charts using a set of simple operators. To support systematic construction while addressing the main challenge of expressive pictorial chart authoring-manual composition and fine-tuning of visual properties-PiCCL introduces a parametric representation that integrates data-driven chart generation with graphical composition. It also employs a lazy data-binding mechanism that automatically synthesizes charts. PiCCL is grounded in a comprehensive analysis of real-world pictorial chart examples. We describe PiCCL's design and its implementation as piccl.js, a JavaScript-based library. To evaluate PiCCL, we showcase a gallery that demonstrates its expressiveness and report findings from a user study assessing the usability of piccl.js. We conclude with a discussion of PiCCL's limitations and potential, as well as future research directions.

Density plots effectively summarize large numbers of points, which would otherwise lead to severe overplotting in, for example, a scatter plot. However, when applied to line-based datasets, such as trajectories or time series, density plots alone are insufficient, as they disrupt path continuity, obscuring smooth trends and rare anomalies. We propose a bin-based illumination model that decouples structure from density to enhance flow and reveal sparse outliers while preserving the original colormap. We introduce a bin-based outlierness metric to rank trajectories. Guided by this ranking, we construct a structural normal map and apply locally-adaptive lighting in the luminance channel to highlight chosen patterns-from dominant trends to atypical paths-with acceptable color distortion. Our interactive method enables analysts to prioritize main trends, focus on outliers, or strike a balance between the two. We demonstrate our method on several real-world datasets, showing it reveals details missed by simpler alternatives, achieves significantly lower CIEDE2000 color distortion than standard shading, and supports interactive updates for up to 10,000 lines.

Traditional force-based graph layout models are rooted in virtual physics, while criteria-driven techniques position nodes by directly optimizing graph readability criteria. In this article, we systematically explore the integration of these two approaches, introducing criteria-driven force-based graph layout techniques. We propose a general framework that, based on user-specified readability criteria, such as minimizing edge crossings, automatically constructs a force-based model tailored to generate layouts for a given graph. Models derived from highly similar graphs can be reused to create initial layouts, users can further refine layouts by imposing different criteria on subgraphs. We perform quantitative comparisons between our layout methods and existing techniques across various graphs and present a case study on graph exploration. Our results indicate that our framework generates superior layouts compared to existing techniques and exhibits better generalization capabilities than deep learning-based methods.

Honorable Mention Award

Typical financial risk management involves distinct phases for pre-service risk assessment and in-service default detection, often modeled separately. This paper proposes a novel framework, Multi-Granularity Knowledge Distillation (abbreviated as MGKD), aimed at improving pre-service risk prediction through the integration of in-service user behavior data. MGKD follows the idea of knowledge distillation, where the teacher model, trained on historical in-service data, guides the student model, which is trained on pre-service data. By using soft labels derived from in-service data, the teacher model helps the student model improve its risk prediction prior to service activation. Meanwhile, a multi-granularity distillation strategy is introduced, including coarse-grained, fine-grained, and self-distillation, to align the representations and predictions of the teacher and student models. This approach not only reinforces the representation of default cases but also enables the transfer of key behavioral patterns associated with defaulters from the teacher to the student model, thereby improving the overall performance of pre-service risk assessment. Moreover, we adopt a re-weighting strategy to mitigate the model's bias towards the minority class. Experimental results on large-scale real-world datasets from Tencent Mobile Payment demonstrate the effectiveness of our proposed approach in both offline and online scenarios.

Graph anomaly detection faces significant challenges due to the scarcity of reliable anomaly-labeled datasets, driving the development of unsupervised methods. Graph autoencoders (GAEs) have emerged as a dominant approach by reconstructing graph structures and node features while deriving anomaly scores from reconstruction errors. However, relying solely on reconstruction error for anomaly detection has limitations, as it increases the sensitivity to noise and overfitting. To address these issues, we propose Graph Evidential Learning (GEL), a probabilistic framework that redefines the reconstruction process through evidential learning. By modeling node features and graph topology using evidential distributions, GEL quantifies two types of uncertainty: graph uncertainty and reconstruction uncertainty, incorporating them into the anomaly scoring mechanism. Extensive experiments demonstrate that GEL achieves state-of-the-art performance while maintaining high robustness against noise and structural perturbations.

Large Language Models (LLMs) face significant limitations when applied to large-scale graphs, struggling with context constraints and inflexible reasoning. We introduce GraphChain, a novel framework enabling LLMs to analyze large graphs by orchestrating dynamic sequences of specialized tools, mimicking human exploratory processes. GraphChain incorporates two core technical contributions: (1) Progressive Graph Distillation, a reinforcement learning approach that learns to generate tool sequences balancing task relevance and intermediate state compression, thereby overcoming LLM context limitations. (2) Structure-aware Test-Time Adaptation (STTA), a mechanism using a lightweight, self-supervised adapter conditioned on graph spectral properties to efficiently adapt a frozen LLM policy to diverse graph structures via soft prompts without retraining. Experiments show GraphChain significantly outperforms prior methods, enabling scalable and adaptive LLM-driven graph analysis.

Graph anomaly detection (GAD) has become a critical research area, with successful applications in financial fraud and telecommunications. Traditional Graph Neural Networks (GNNs) face significant challenges: at the topology level, they suffer from over-smoothing that averages out anomalous signals; at the feature level, discriminative models struggle when fraudulent nodes obfuscate their features to evade detection. In this paper, we propose a Conditional Graph Anomaly Diffusion Model (CGADM) that addresses these issues through the iterative refinement and denoising reconstruction properties of diffusion models. Our approach incorporates a prior-guided diffusion process that injects a pre-trained conditional anomaly estimator into both forward and reverse diffusion chains, enabling more accurate anomaly detection. For computational efficiency on large-scale graphs, we introduce a prior confidence-aware mechanism that adaptively determines the number of reverse denoising steps based on prior confidence. Experimental results on benchmark datasets demonstrate that CGADM achieves state-of-the-art performance while maintaining significant computational advantages for large-scale graph applications.

Visual analysis of large time-series data often requires transformations over multivariate time series. Existing methods struggle to meet interactive response time requirements, relying on full transformations that incur high computation costs. We propose a visualization-oriented transformation system PIVOT that incrementally generates accurate visualizations by selectively transforming only essential data samples. At its core is a transformation-aware query mechanism that efficiently computes point-wise transformations by leveraging cached hierarchical data on the server. To support responsive interaction, we introduce a pixel-based error-bound guarantee that estimates the accuracy of intermediate visualizations without requiring a reference, enabling a balance between latency and visual fidelity. Experiments show that PIVOT achieves highly accurate visualizations with interactive response times, outperforming existing error-free methods by up to an order of magnitude on billion-scale datasets.

Data science pipelines consist of data preprocessing and transformation, and a typical pipeline comprises a series of operators, such as DataFrame filtering and groupby. As practitioners seek tools to handle larger-scale data while maintaining APIs compatible with popular single-machine libraries (e.g., pandas), scaling such a pipeline requires efficient distribution of decomposed tasks across the cluster and fine-grained, key-level intermediate storage management, two challenges that existing systems have not effectively addressed. Motivated by the requirements of scaling diverse data science applications, we present the design and implementation of Xorbits, a native scalable data science engine built on our decentralized actor model, Xoscar. Our actor model can eliminate dependency on a global scheduler and enable fast actor task scheduling. We also provide reference-based distributed storage with unified access across heterogeneous memory resources. Our evaluation demonstrates that Xorbits achieves up to 3.22X speedup on 3 machine learning pipelines and 22 data analysis workloads compared to state-of-the-art solutions. Xorbits is available on PyPI with nearly 1k daily downloads and has been successfully deployed in production environments.

We present a novel visualization-driven illumination model for density plots, a new technique to enhance density plots by effectively revealing the detailed structures in high- and medium-density regions and outliers in low-density regions, while avoiding artifacts in the density field's colors. When visualizing large and dense discrete point samples, scatterplots and dot density maps often suffer from overplotting, and density plots are commonly employed to provide aggregated views while revealing underlying structures. Yet, in such density plots, existing illumination models may produce color distortion and hide details in low-density regions, making it challenging to look up density values, compare them, and find outliers. The key novelty in this work includes (i) a visualization-driven illumination model that inherently supports density-plot-specific analysis tasks and (ii) a new image composition technique to reduce the interference between the image shading and the color-encoded density values. To demonstrate the effectiveness of our technique, we conducted a quantitative study, an empirical evaluation of our technique in a controlled study, and two case studies, exploring twelve datasets with up to two million data point samples.

This article presents a systematic study of the generalization of convolutional neural networks (CNNs) and humans on relational reasoning tasks with bar charts. We first revisit previous experiments on graphical perception and update the benchmark performance of CNNs. We then test the generalization performance of CNNs on a classic relational reasoning task: estimating bar length ratios in a bar chart, by progressively perturbing the standard visualizations. We further conduct a user study to compare the performance of CNNs and humans. Our results show that CNNs outperform humans only when the training and test data have the same visual encodings. Otherwise, they may perform worse. We also find that CNNs are sensitive to perturbations in various visual encodings, regardless of their relevance to the target bars. Yet, humans are mainly influenced by bar lengths. Our study suggests that robust relational reasoning with visualizations is challenging for CNNs. Improving CNNs' generalization performance may require training them to better recognize task-related visual properties.

Transparency is commonly utilized in visualizations to overlay color-coded histograms or sets, thereby facilitating the visual comparison of categorical data. However, these charts often suffer from significant overlap between objects, resulting in substantial color interactions. Existing color blending models struggle in these scenarios, frequently leading to ambiguous color mappings and the introduction of false colors. To address these challenges, we propose an automated approach for generating optimal color encodings to enhance the perception of translucent charts. Our method harnesses color nameability to maximize the association between composite colors and their respective class labels. We introduce a color-name aware (CNA) optimization framework that generates maximally coherent color assignments and transparency settings while ensuring perceptual discriminability for all segments in the visualization. We demonstrate the effectiveness of our technique through crowdsourced experiments with composite histograms, showing how our technique can significantly outperform both standard and visualization-specific color blending models. Furthermore, we illustrate how our approach can be generalized to other visualizations, including parallel coordinates and Venn diagrams. We provide an open-source implementation of our technique as a web-based tool.

We present an authoring tool, called CAST+ (Canis Studio Plus), that enables the interactive creation of chart animations through the direct manipulation of keyframes. It introduces the visual specification of chart animations consisting of keyframes that can be played sequentially or simultaneously, and animation parameters (e.g., duration, delay). Building on Canis (Ge et al. 2020), a declarative chart animation grammar that leverages data-enriched SVG charts, CAST+ supports auto-completion for constructing both keyframes and keyframe sequences. It also enables users to refine the animation specification (e.g., aligning keyframes across tracks to play them together, adjusting delay) with direct manipulation. We report a user study conducted to assess the visual specification and system usability with its initial version. We enhanced the system's expressiveness and usability: CAST+ now supports the animation of multiple types of visual marks in the same keyframe group with new auto-completion algorithms based on generalized selection. This enables the creation of more expressive animations, while reducing the number of interactions needed to create comparable animations. We present a gallery of examples and four usage scenarios to demonstrate the expressiveness of CAST+. Finally, we discuss the limitations, comparison, and potentials of CAST+ as well as directions for future research.

A safety boundary wall in VR is a virtual barrier that defines a safe area, allowing users to navigate and interact without safety concerns. However, existing implementations neglect to utilize the safety boundary wall's large surface for displaying interactive information. In this work, we propose the BoundaryScreen technique based on the "walking outward" metaphor to add interactivity to the safety boundary wall. Specifically, we augment the safety boundary wall by placing the home screen on it. To summon the home screen, the user only needs to walk outward until it appears. Results showed that (i) participants significantly preferred BoundaryScreen in the outermost two-step-wide ring-shaped section of a circular safety area; and (ii) participants exhibited strong "behavioral inertia" for walking, i.e., after completing a routine activity involving constant walking, participants significantly preferred to use the walking-based BoundaryScreen technique to summon the home screen.

Point cloud completion aims to infer a complete shape from its partial observation. Many approaches utilize a pure encoder-decoder paradigm in which complete shape can be directly predicted by shape priors learned from partial scans, however, these methods suffer from the loss of details inevitably due to the feature abstraction issues. In this paper, we propose a novel framework, termed SPAC-Net, that aims to rethink the completion task under the guidance of a new structural prior, we call it interface. Specifically, our method first investigates Marginal Detector (MAD) module to localize the interface, defined as the intersection between the known observation and the missing parts. Based on the interface, our method predicts the coarse shape by learning the displacement from the points in interface move to their corresponding position in missing parts. Furthermore, we devise an additional Structure Supplement (SSP) module before the upsampling stage to enhance the structural details of the coarse shape, enabling the upsampling module to focus more on the upsampling task. Extensive experiments have been conducted on several challenging benchmarks, and the results demonstrate that our method outperforms existing state-of-the-art approaches.

Recently, significant progress has been made in condition-guided human motion generation. However, due to the inherent abstraction of conditional semantics like text, music and trajectory, these methods often fall short of generating precise motions that align with human intent. In contrast, free-hand sketches inherently and accurately depict human perspective intent, finding extensive applications across multiple domains. In this article, we introduce Sketch-guided human Motion Diffusion (SMD), to address a novel scenario: sketch-to-motion, aiming to generate plausible and natural human motions based on human motion sketches. Specifically, Our proposed SMD employs a Dual-branch Time-aware Transformer that utilizes both global semantic and local perspective level attention to condition 2D sketch information for 3D motion generation. At the global semantic level, we establish associations between the representation of the entire sketch and the sequential motion to ensure the generated motion aligns with the semantic content of the sketch. Meanwhile, at the local perspective level, a sketch-aware local attention is devised to correlate the sketch patches with the motion keyframes, aiming to precisely align the keyframes with the given sketches. Rooted in Diffusion model and Dual-branch Time-aware Transformer, our approach demonstrates proficiency in motion in-betweening and body part editing tasks, seamlessly generating natural motion sequences that harmonize with the provided context. Multiple experiments conducted on the curated sketch-to-motion datasets validate the efficacy of SMD, showcasing the state-of-the-art generation performances.

Quantitative data is frequently represented using color, yet designing effective color mappings is a challenging task, requiring one to balance perceptual standards with personal color preference. Current design tools either overwhelm novices with complexity or offer limited customization options. We present ColorMaker, a mixed-initiative approach for creating colormaps. ColorMaker combines fluid user interaction with real-time optimization to generate smooth, continuous color ramps. Users specify their loose color preferences while leaving the algorithm to generate precise color sequences, meeting both designer needs and established guidelines. ColorMaker can create new colormaps, including designs accessible for people with color-vision deficiencies, starting from scratch or with only partial input, thus supporting ideation and iterative refinement. We show that our approach can generate designs with similar or superior perceptual characteristics to standard colormaps. A user study demonstrates how designers of varying skill levels can use this tool to create custom, high-quality colormaps. ColorMaker is available at: colormaker.org

To facilitate the reuse of existing charts, previous research has examined how to obtain a semantic understanding of a chart by deconstructing its visual representation into reusable components, such as encodings. However, existing deconstruction approaches primarily focus on chart styles, handling only basic layouts. In this paper, we investigate how to deconstruct chart layouts, focusing on rectangle-based ones, as they cover not only 17 chart types but also advanced layouts (e.g., small multiples, nested layouts). We develop an interactive tool, called Mystique, adopting a mixed-initiative approach to extract the axes and legend, and deconstruct a chart's layout into four semantic components: mark groups, spatial relationships, data encodings, and graphical constraints. Mystique employs a wizard interface that guides chart authors through a series of steps to specify how the deconstructed components map to their own data. On 150 rectangle-based SVG charts, Mystique achieves above 85% accuracy for axis and legend extraction and 96% accuracy for layout deconstruction. In a chart reproduction study, participants could easily reuse existing charts on new datasets. We discuss the current limitations of Mystique and future research directions.

NJ) trees as a new way to visually explore cluster structures and outliers in multi-dimensional data. Neighbor-joining (NJ) trees are widely used in biology, and their visual representation is similar to that of dendrograms. The core difference to dendrograms, however, is that NJ trees correctly encode distances between data points, resulting in trees with varying edge lengths. We optimize NJ trees for their use in visual analysis in two ways. First, we propose to use a novel leaf sorting algorithm that helps users to better interpret adjacencies and proximities within such a tree. Second, we provide a new method to visually distill the cluster tree from an ordered NJ tree. Numerical evaluation and three case studies illustrate the benefits of this approach for exploring multi-dimensional data in areas such as biology or image analysis.

Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of underlying trends in complex datasets. Thus, we propose a novel image space coloring method for line-based density plots that enhances their interpretability. Our method employs color not only to visually communicate data density but also to highlight similar regions in the plot, allowing users to identify and distinguish trends easily. We achieve this by performing hierarchical clustering based on the lines passing through each region and mapping the identified clusters to the hue circle using circular MDS. Additionally, we propose a heuristic approach to assign each line to the most probable cluster, enabling users to analyze density and individual lines. We motivate our method by conducting a small-scale user study, demonstrating the effectiveness of our method using synthetic and real-world datasets, and providing an interactive online tool for generating colored line-based density plots.

In this article, we propose the t-FDP model, a force-directed placement method based on a novel bounded short-range force (t-force) defined by Student's t-distribution. Our formulation is flexible, exerts limited repulsive forces for nearby nodes and can be adapted separately in its short- and long-range effects. Using such forces in force-directed graph layouts yields better neighborhood preservation than current methods, while maintaining low stress errors. Our efficient implementation using a Fast Fourier Transform is one order of magnitude faster than state-of-the-art methods and two orders faster on the GPU, enabling us to perform parameter tuning by globally and locally adjusting the t-force in real-time for complex graphs. We demonstrate the quality of our approach by numerical evaluation against state-of-the-art approaches and extensions for interactive exploration.

Color is one of the main visual channels used for highlighting elements of interest in visualization. However, in multi-class scatterplots, color highlighting often comes at the expense of degraded color discriminability. In this paper, we argue for context-preserving highlighting during the interactive exploration of multi-class scatterplots to achieve desired pop-out effects, while maintaining good perceptual separability among all classes and consistent color mapping schemes under varying points of interest. We do this by first generating two contrastive color mapping schemes with large and small contrasts to the background. Both schemes maintain good perceptual separability among all classes and ensure that when colors from the two palettes are assigned to the same class, they have a high color consistency in color names. We then interactively combine these two schemes to create a dynamic color mapping for highlighting different points of interest. We demonstrate the effectiveness through crowd-sourced experiments and case studies.

In this paper, we propose a correlation-aware probabilistic data summarization technique to efficiently analyze and visualize large-scale multi-block volume data generated by massively parallel scientific simulations. The core of our technique is correlation modeling of distribution representations of adjacent data blocks using copula functions and accurate data value estimation by combining numerical information, spatial location, and correlation distribution using Bayes’ rule. This effectively preserves statistical properties without merging data blocks in different parallel computing nodes and repartitioning them, thus significantly reducing the computational cost. Furthermore, this enables reconstruction of the original data more accurately than existing methods. We demonstrate the effectiveness of our technique using six datasets, with the largest having one billion grid points. The experimental results show that our approach reduces the data storage cost by approximately one order of magnitude compared to state-of-the-art methods while providing a higher reconstruction accuracy at a lower computational cost.

We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.

We present a novel multi-level representation of time series called OM3 that facilitates efficient interactive progressive visualization of large data stored in a database and supports various interactions such as resizing, panning, zooming, and visual query. Based on our proposed line-segment aggregation, this representation can produce error-free line visualizations that preserve the shape of a time series in windows of arbitrary sizes. To reduce the interaction latency, we develop an incremental tree-based query strategy to support progressive visualizations, allowing a finer control on the accuracy-time tradeoff. We quantitatively compare OM3 with state-of-the-art methods, including a method implemented on a leading time-series database InfluxDB, in two settings with databases residing either in the local area network or on the cloud. Results show that OM^3 maintains a low latency within 300~ms on the web browser and a high data reduction ratio regardless of the data size (ranging from millions to billions of records), achieving around 1,000 times faster than the state-of-the-art methods on the largest dataset experimented with.

We present SizePairs, a new technique to create stable and balanced treemap layouts that visualize values changing over time in hierarchical data. To achieve an overall high-quality result across all time steps in terms of stability and aspect ratio, SizePairs employs a new hierarchical size-based pairing algorithm that recursively pairs two nodes that complement their size changes over time and have similar sizes. SizePairs maximizes the visual quality and stability by optimizing the splitting orientation of each internal node and flipping leaf nodes, if necessary. We also present a comprehensive comparison of SizePairs against the state-of-the-art treemaps developed for visualizing time-dependent data. SizePairs outperforms existing techniques in both visual quality and stability, while being faster than the local moves technique.

We present Target Netgrams as a visualization technique for radial layouts of graphs. Inspired by manually created target sociograms, we propose an annulus-constrained stress model that aims to position nodes onto the annuli between adjacent circles for indicating their radial hierarchy, while maintaining the network structure (clusters and neighborhoods) and improving readability as much as possible. This is achieved by having more space on the annuli than traditional layout techniques. By adapting stress majorization to this model, the layout is computed as a constrained least square optimization problem. Additional constraints (e.g., parent-child preservation, attribute-based clusters and structure-aware radii) are provided for exploring nodes, edges, and levels of interest. We demonstrate the effectiveness of our method through a comprehensive evaluation, a user study, and a case study.

Over the past few decades, a large number of graph layout techniques have been proposed for visualizing graphs from various domains. In this paper, we present a general framework, Taurus, for unifying popular techniques such as the spring-electrical model, stress model, and maxent-stress model. It is based on a unified force representation, which formulates most existing techniques as a combination of quotient-based forces that combine power functions of graph-theoretical and Euclidean distances. This representation enables us to compare the strengths and weaknesses of existing techniques, while facilitating the development of new methods. Based on this, we propose a new balanced stress model (BSM) that is able to layout graphs in superior quality. In addition, we introduce a universal augmented stochastic gradient descent (SGD) optimizer that efficiently finds proper solutions for all layout techniques. To demonstrate the power of our framework, we conduct a comprehensive evaluation of existing techniques on a large number of synthetic and real graphs. We release an open-source package, which facilitates easy comparison of different graph layout methods for any graph input as well as effectively creating customized graph layout techniques.

With the development of virtual reality, the practical requirements of the wearable haptic interface have been greatly emphasized. While passive haptic devices are commonly used in virtual reality, they lack generality and are difficult to precisely generate continuous force feedback to users. In this work, we present SmartSpring, a new solution for passive haptics, which is inexpensive, lightweight and capable of providing controllable force feedback in virtual reality. We propose a hybrid spring-linkage structure as the proxy and flexibly control the mechanism for adjustable system stiffness. By analyzing the structure and force model, we enable a smart transform of the structure for producing continuous force signals. We quantitatively examine the real-world performance of SmartSpring to verify our model. By asymmetrically moving or actively pressing the end-effector, we show that our design can further support rendering torque and stiffness. Finally, we demonstrate the SmartSpring in a series of scenarios with user studies and a just noticeable difference analysis. Experimental results show the potential of the developed haptic display in virtual reality.

One main challenge for simplifying node-link diagrams of large-scale social networks lies in that simplified graphs generally contain dense subgroups or cohesive subgraphs. Graph triangles quantify the solid and stable relationships that maintain cohesive subgraphs. Understanding the mechanism of triangles within cohesive subgraphs contributes to illuminating patterns of connections within social networks. However, prior works can hardly handle and visualize triangles in cohesive subgraphs. In this paper, we propose a triangle-based graph simplification approach that can filter and visualize cohesive subgraphs by leveraging a triangle-connectivity called k-truss and a force-directed algorithm. We design and implement TriGraph, a web-based visual interface that provides detailed information for exploring and analyzing social networks. Quantitive comparions with existing methods, two case studies on real-world datasets, and the feedback from domain experts demonstrate the effectiveness of TriGraph.

We present a pyramid-based scatterplot sampling technique to avoid overplotting and enable progressive and streaming visualization of large data. Our technique is based on a multiresolution pyramid-based decomposition of the underlying density map and makes use of the density values in the pyramid to guide the sampling at each scale for preserving the relative data densities and outliers. We show that our technique is competitive in quality with state-of-the-art methods and runs faster by about an order of magnitude. Also, we have adapted it to deliver progressive and streaming data visualization by processing the data in chunks and updating the scatterplot areas with visible changes in the density map. A quantitative evaluation shows that our approach generates stable and faithful progressive samples that are comparable to the state-of-the-art method in preserving relative densities and superior to it in keeping outliers and stability when switching frames. We present two case studies that demonstrate the effectiveness of our approach for exploring large data.

Creating comprehensible visualizations of highly overlapping set-typed data is a challenging task due to its complexity. To facilitate insights into set connectivity and to leverage semantic relations between intersections, we propose a fast two-step layout technique for Euler diagrams that are both well-matched and well-formed. Our method conforms to established form guidelines for Euler diagrams regarding semantics, aesthetics, and readability. First, we establish an initial ordering of the data, which we then use to incrementally create a planar, connected, and monotone dual graph representation. In the next step, the graph is transformed into a circular layout that maintains the semantics and yields simple Euler diagrams with smooth curves. When the data cannot be represented by simple diagrams, our algorithm always falls back to a solution that is not well-formed but still well-matched, whereas previous methods often fail to produce expected results. We show the usefulness of our method for visualizing set-typed data using examples from text analysis and infographics. Furthermore, we discuss the characteristics of our approach and evaluate our method against state-of-the-art methods.

We present Joint t-Stochastic Neighbor Embedding (Joint t-SNE), a technique to generate comparable projections of multiple high-dimensional datasets. Although t-SNE has been widely employed to visualize high-dimensional datasets from various domains, it is limited to projecting a single dataset. When a series of high-dimensional datasets, such as datasets changing over time, is projected independently using t-SNE, misaligned layouts are obtained. Even items with identical features across datasets are projected to different locations, making the technique unsuitable for comparison tasks. To tackle this problem, we introduce edge similarity, which captures the similarities between two adjacent time frames based on the Graphlet Frequency Distribution (GFD). We then integrate a novel loss term into the t-SNE loss function, which we call vector constraints, to preserve the vectors between projected points across the projections, allowing these points to serve as visual landmarks for direct comparisons between projections. Using synthetic datasets whose ground-truth structures are known, we show that Joint t-SNE outperforms existing techniques, including Dynamic t-SNE, in terms of local coherence error, Kullback-Leibler divergence, and neighborhood preservation. We also showcase a real-world use case to visualize and compare the activation of different layers of a neural network.

In this paper, we propose F2-Bubbles, a set overlay visualization technique that addresses overlapping artifacts and supports interactive editing with intelligent suggestions. The core of our method is a new, efficient set overlay construction algorithm that approximates the optimal set overlay by considering set elements and their non-set neighbors. Thanks to the efficiency of the algorithm, interactive editing is achieved, and with intelligent suggestions, users can easily and flexibly edit visualizations through direct manipulations with local adaptations. A quantitative comparison with state-of-the-art set visualization techniques and case studies demonstrate the effectiveness of our method and suggests that F2-Bubbles is a helpful technique for set visualization.

Dimensionality Reduction (DR) techniques can generate 2D projections and enable visual exploration of cluster structures of high-dimensional datasets. However, different DR techniques would yield various patterns, which significantly affect the performance of visual cluster analysis tasks. We present the results of a user study that investigates the influence of different DR techniques on visual cluster analysis. Our study focuses on the most concerned property types, namely the linearity and locality, and evaluates twelve representative DR techniques that cover the concerned properties. Four controlled experiments were conducted to evaluate how the DR techniques facilitate the tasks of 1) cluster identification, 2) membership identification, 3) distance comparison, and 4) density comparison, respectively. We also evaluated users' subjective preference of the DR techniques regarding the quality of projected clusters. The results show that: 1) Non-linear and Local techniques are preferred in cluster identification and membership identification; 2) Linear techniques perform better than non-linear techniques in density comparison; 3) UMAP (Uniform Manifold Approximation and Projection) and t-SNE (t-Distributed Stochastic Neighbor Embedding) perform the best in cluster identification and membership identification; 4) NMF (Nonnegative Matrix Factorization) has competitive performance in distance comparison; 5) t-SNLE (t-Distributed Stochastic Neighbor Linear Embedding) has competitive performance in density comparison.

Colormapping is an effective and popular visualization technique for analyzing patterns in scalar fields. Scientists usually adjust a default colormap to show hidden patterns by shifting the colors in a trial-and-error process. To improve efficiency, efforts have been made to automate the colormap adjustment process based on data properties (e.g., statistical data value or histogram distribution). However, as the data properties have no direct correlation to the spatial variations, previous methods may be insufficient to reveal the dynamic range of spatial variations hidden in the data. To address the above issues, we conduct a pilot analysis with domain experts and summarize three requirements for the colormap adjustment process. Based on the requirements, we formulate colormap adjustment as an objective function, composed of a boundary term and a fidelity term, which is flexible enough to support interactive functionalities. We compare our approach with alternative methods under a quantitative measure and a qualitative user study (25 participants), based on a set of data with broad distribution diversity. We further evaluate our approach via three case studies with six domain experts. Our method is not necessarily more optimal than alternative methods of revealing patterns, but rather is an additional color adjustment option for exploring data with a dynamic range of spatial variations.

Time-series data-usually presented in the form of lines-plays an important role in many domains such as finance, meteorology, health, and urban informatics. Yet, little has been done to support interactive exploration of large-scale time-series data, which requires a clutter-free visual representation with low-latency interactions. In this paper, we contribute a novel line-segment-based KD-tree method to enable interactive analysis of many time series. Our method enables not only fast queries over time series in selected regions of interest but also a line splatting method for efficient computation of the density field and selection of representative lines. Further, we develop KD-Box, an interactive system that provides rich interactions, e.g., timebox, attribute filtering, and coordinated multiple views. We demonstrate the effectiveness of KD-Box in supporting efficient line query and density field computation through a quantitative comparison and show its usefulness for interactive visual analysis on several real-world datasets.

We present CAST, an authoring tool that enables the interactive creation of chart animations. It introduces the visual specification of chart animations consisting of keyframes that can be played sequentially or simultaneously, and animation parameters (e.g., duration, delay). Building on Canis [19], a declarative chart animation grammar that leverages data-enriched SVG charts, CAST supports auto-completion for constructing both keyframes and keyframe sequences. It also enables users to refine the animation specification (e.g., aligning keyframes across tracks to play them together, adjusting delay) with direct manipulation and other parameters for animation effects (e.g., animation type, easing function) using a control panel. In addition to describing how CAST infers recommendations for auto-completion, we present a gallery of examples to demonstrate the expressiveness of CAST and a user study to verify its learnability and usability. Finally, we discuss the limitations and potentials of CAST as well as directions for future research.

A common task for scatterplots is communicating trends in bivariate data. However, the ability of people to visually estimate these trends is under-explored, especially when the data violate assumptions required for common statistical models, or visual trend estimates are in conflict with statistical ones. In such cases, designers may need to intervene and de-bias these estimations, or otherwise inform viewers about differences between statistical and visual trend estimations. We propose data-driven mark orientation as a solution in such cases, where the directionality of marks in the scatterplot guide participants when visual estimation is otherwise unclear or ambiguous. Through a set of laboratory studies, we investigate trend estimation across a variety of data distributions and mark directionalities, and find that data-driven mark orientation can help resolve ambiguities in visual trend estimates.

Scribble-supervised semantic segmentation has gained much attention recently for its promising performance without high-quality annotations. Due to the lack of supervision, confident and consistent predictions are usually hard to obtain. Typically, people handle these problems by either adopting an auxiliary task with the well-labeled dataset or incorporating a graphical model with additional requirements on scribble annotations. Instead, this work aims to achieve semantic segmentation by scribble annotations directly without extra information and other limitations. Specifically, we propose holistic operations, including minimizing entropy and a network embedded random walk on the neural representation to reduce uncertainty. Given the probabilistic transition matrix of a random walk, we further train the network with self-supervision on its neural eigenspace to impose consistency on predictions between related images. Comprehensive experiments and ablation studies verify the proposed approach, which demonstrates superiority over others; it is even comparable to some full-label supervised ones and works well when scribbles are randomly shrunk or dropped.

A common enhancement of scatterplots represents points as small multiples, glyphs, or thumbnail images. As this encoding often results in overlaps, a general strategy is to alter the position of the data points, for instance, to a grid-like structure. Previous approaches rely on solving expensive optimization problems or on dividing the space that alter the global structure of the scatterplot. To find a good balance between efficiency and neighborhood and layout preservation, we propose Hagrid, a technique that uses space-filling curves (SFCs) to “gridify” a scatterplot without employing expensive collision detection and handling mechanisms. Using SFCs ensures that the points are plotted close to their original position, retaining approximately the same global structure. The resulting scatterplot is mapped onto a rectangular or hexagonal grid, using Hilbert and Gosper curves. We discuss and evaluate the theoretic runtime of our approach and quantitatively compare our approach to three state-of-the-art gridifying approaches, DGrid, Small multiples with gaps SMWG, and CorrelatedMultiples CMDS, in an evaluation comprising 339 scatterplots. Here, we compute several quality measures for neighborhood preservation together with an analysis of the actual runtimes. The main results show that, compared to the best other technique, Hagrid is faster by a factor of four, while achieving similar or even better quality of the gridified layout. Due to its computational efficiency, our approach also allows novel applications of gridifying approaches in interactive settings, such as removing local overlap upon hovering over a scatterplot.

2D sketch-based tree modeling cannot guarantee to generate plausible depth values and full 3D tree shapes. With the advent of virtual reality (VR) technologies, 3D sketching enables a new form for 3D tree modeling. However, it is labor-intensive and difficult to create realistically-looking 3D trees with complicated geometry and lots of detailed twigs with a reasonable amount of effort. In this paper, we explore the use of mid-air finger 3D sketching in VR for tree modeling. We present a hybrid approach that integrates freehand 3D sketches with an automatic population of branch geometries. The user only needs to draw a few 3D strokes in mid-air to define the envelope of the foliage (denoted as lobes) and main branches. Our algorithm then automatically generates a full 3D tree model based on these stroke inputs. Additionally, the shape of the 3D tree model can be modified by freely dragging, squeezing, or moving lobes in mid-air. We demonstrate the ease-of-use, efficiency, and flexibility in tree modeling and overall shape control. We perform user studies and show a variety of realistic tree models generated instantaneously from 3D finger sketching.

Abstract The Manhattan‐world building is a kind of dominant scene in urban areas. Many existing methods for reconstructing such scenes are either vulnerable to noisy and incomplete data or suffer from high computational complexity. In this paper, we present a novel approach to quickly reconstruct lightweight Manhattan‐world urban building models from images. Our key idea is to reconstruct buildings through the salient feature ‐ corners. Given a set of urban building images, Structure‐from‐Motion and 3D line reconstruction operations are applied first to recover camera poses, sparse point clouds, and line clouds. Then we use orthogonal planes detected from the line cloud to generate corners, which indicate a part of possible buildings. Starting from the corners, we fit cubes to point clouds by optimizing corner parameters and obtain cube representations of corresponding buildings. Finally, a registration step is performed on cube representations to generate more accurate models. Experiment results show that our approach can handle some nasty cases containing noisy and incomplete data, meanwhile, output lightweight polygonal building models with a low time‐consuming.

Abstract We introduce the curve complexity heuristic (CCH), a KD‐tree construction strategy for 3D curves, which enables interactive exploration of neighborhoods in dense and large line datasets. It can be applied to searches of k‐nearest curves (KNC) as well as radius‐nearest curves (RNC). The CCH KD‐tree construction consists of two steps: (i) 3D curve decomposition that takes into account curve complexity and (ii) KD‐tree construction, which involves a novel splitting and early termination strategy. The obtained KD‐tree allows us to improve the speed of existing neighborhood search approaches by at least an order of magnitude (i. e., 28×for KNC and 12×for RNC with 98% accuracy) by considering local curve complexity. We validate this performance with a quantitative evaluation of the quality of search results and computation time. Also, we demonstrate the usefulness of our approach for supporting various applications such as interactive line queries, line opacity optimization, and line abstraction.

三元空间大数据一般定义为由其定义领域 (包括数据、 对象、 任务、 应用场景、 主体等) 所有元素组成的集合. 可视分析是一种新兴的人在回路大数据分析范式, 可利用人类感知提高人类认知效率. 本文探讨三元空间大数据跨域可视化分析, 强调三元空间大数据跨域性带来的新挑战——数据、 主题和任务域, 并提出一个新的可视分析模型和一套方法来应对这些挑战.

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.

In this paper, we propose SineStream, a new variant of streamgraphs that improves their readability by minimizing sine illusion effects. Such effects reflect the tendency of humans to take the orthogonal rather than the vertical distance between two curves as their distance. In SineStream, we connect the readability of streamgraphs with minimizing sine illusions and by doing so provide a perceptual foundation for their design. As the geometry of a streamgraph is controlled by its baseline (the bottom-most curve) and the ordering of the layers, we re-interpret baseline computation and layer ordering algorithms in terms of reducing sine illusion effects. For baseline computation, we improve previous methods by introducing a Gaussian weight to penalize layers with large thickness changes. For layer ordering, three design requirements are proposed and implemented through a hierarchical clustering algorithm. Quantitative experiments and user studies demonstrate that SineStream improves the readability and aesthetics of streamgraphs compared to state-of-the-art methods.

We present an integrated approach for creating and assigning color palettes to different visualizations such as multi-class scatterplots, line, and bar charts. While other methods separate the creation of colors from their assignment, our approach takes data characteristics into account to produce color palettes, which are then assigned in a way that fosters better visual discrimination of classes. To do so, we use a customized optimization based on simulated annealing to maximize the combination of three carefully designed color scoring functions: point distinctness, name difference, and color discrimination. We compare our approach to state-of-the-art palettes with a controlled user study for scatterplots and line charts, furthermore we performed a case study. Our results show that Palettailor, as a fully-automated approach, generates color palettes with a higher discrimination quality than existing approaches. The efficiency of our optimization allows us also to incorporate user modifications into the color selection process.

We propose a new method to tackle the mapping challenge from time-series data to spatial image in the field of seismic exploration, i.e., reconstructing the velocity model directly from seismic data by deep neural networks (DNNs). The conventional way of addressing this ill-posed inversion problem is through iterative algorithms, which suffer from poor nonlinear mapping and strong nonuniqueness. Other attempts may either import human intervention errors or underuse seismic data. The challenge for DNNs mainly lies in the weak spatial correspondence, the uncertain reflection-reception relationship between seismic data and velocity model, as well as the time-varying property of seismic data. To tackle these challenges, we propose end-to-end seismic inversion networks (SeisInvNets) with novel components to make the best use of all seismic data. Specifically, we start with every seismic trace and enhance it with its neighborhood information, its observation setup, and the global context of its corresponding seismic profile. From the enhanced seismic traces, the spatially aligned feature maps can be learned and further concatenated to reconstruct a velocity model. In general, we let every seismic trace contribute to the reconstruction of the whole velocity model by finding spatial correspondence. The proposed SeisInvNet consistently produces improvements over the baselines and achieves promising performance on our synthesized and proposed SeisInv data set according to various evaluation metrics. The inversion results are more consistent with the target from the aspects of velocity values, subsurface structures, and geological interfaces. Moreover, the mechanism and the generalization of the proposed method are discussed and verified. Nevertheless, the generalization of deep-learning-based inversion methods on real data is still challenging and considering physics may be one potential solution.

We present a non-uniform recursive sampling technique for multi-class scatterplots, with the specific goal of faithfully presenting relative data and class densities, while preserving major outliers in the plots. Our technique is based on a customized binary kd-tree, in which leaf nodes are created by recursively subdividing the underlying multi-class density map. By backtracking, we merge leaf nodes until they encompass points of all classes for our subsequently applied outlier-aware multi-class sampling strategy. A quantitative evaluation shows that our approach can better preserve outliers and at the same time relative densities in multi-class scatterplots compared to the previous approaches, several case studies demonstrate the effectiveness of our approach in exploring complex and real world data.

We present a new technique to enable the creation of shape-bounded Wordles, we call ShapeWordle, in which we fit words to form a given shape. To guide word placement within a shape, we extend the traditional Archimedean spirals to be shape-aware by formulating the spirals in a differential form using the distance field of the shape. To handle non-convex shapes, we introduce a multi-centric Wordle layout method that segments the shape into parts for our shape-aware spirals to adaptively fill the space and generate word placements. In addition, we offer a set of editing interactions to facilitate the creation of semantically-meaningful Wordles. Lastly, we present three evaluations: a comprehensive comparison of our results against the state-of-the-art technique (WordArt), case studies with 14 users, and a gallery to showcase the coverage of our technique.

In this paper, we examine the robustness of scagnostics through a series of theoretical and empirical studies. First, we investigate the sensitivity of scagnostics by employing perturbing operations on more than 60M synthetic and real-world scatterplots. We found that two scagnostic measures, Outlying and Clumpy, are overly sensitive to data binning. To understand how these measures align with human judgments of visual features, we conducted a study with 24 participants, which reveals that i) humans are not sensitive to small perturbations of the data that cause large changes in both measures, and ii) the perception of clumpiness heavily depends on per-cluster topologies and structures. Motivated by these results, we propose Robust Scagnostics (RScag) by combining adaptive binning with a hierarchy-based form of scagnostics. An analysis shows that RScag improves on the robustness of original scagnostics, aligns better with human judgments, and is equally fast as the traditional scagnostic measures.

Many edge bundling techniques (i.e., data simplification as a support for data visualization and decision making) exist but they are not directly applicable to any kind of dataset and their parameters are often too abstract and difficult to set up. As a result, this hinders the user ability to create efficient aggregated visualizations. To address these issues, we investigated a novel way of handling visual aggregation with a task-driven and user-centered approach. Given a graph, our approach produces a decluttered view as follows: first, the user investigates different edge bundling results and specifies areas, where certain edge bundling techniques would provide user-desired results. Second, our system then computes a smooth and structural preserving transition between these specified areas. Lastly, the user can further fine-tune the global visualization with a direct manipulation technique to remove the local ambiguity and to apply different visual deformations. In this paper, we provide details for our design rationale and implementation. Also, we show how our algorithm gives more suitable results compared to current edge bundling techniques, and in the end, we provide concrete instances of usages, where the algorithm combines various edge bundling results to support diverse data exploration and visualizations.

Since multiple criteria can be adopted to estimate the similarity among the given data points, problem regarding diverse representations of pairwise relations is brought about. To address this issue, a novel self-adaptive multimeasure (SAMM) fusion problem is proposed, such that different measure functions can be adaptively merged into a unified similarity measure. Different from other approaches, we optimize similarity as a variable instead of presetting it as a priori, such that similarity can be adaptively evaluated based on integrating various measures. To further obtain the associated subspace representation, a graph-based dimensionality reduction problem is incorporated into the proposed SAMM problem, such that the related subspace can be achieved according to the unified similarity. In addition, sparsity-inducing ℓ2,0regularization is introduced, such that a sparse projection is obtained for efficient feature selection (FS). Consequently, the SAMM-FS method can be summarized correspondingly.

Appropriate choice of colors significantly aids viewers in understanding the structures in multiclass scatterplots and becomes more important with a growing number of data points and groups. An appropriate color mapping is also an important parameter for the creation of an aesthetically pleasing scatterplot. Currently, users of visualization software routinely rely on color mappings that have been pre-defined by the software. A default color mapping, however, cannot ensure an optimal perceptual separability between groups, and sometimes may even lead to a misinterpretation of the data. In this paper, we present an effective approach for color assignment based on a set of given colors that is designed to optimize the perception of scatterplots. Our approach takes into account the spatial relationships, density, degree of overlap between point clusters, and also the background color. For this purpose, we use a genetic algorithm that is able to efficiently find good color assignments. We implemented an interactive color assignment system with three extensions of the basic method that incorporates top K suggestions, user-defined color subsets, and classes of interest for the optimization. To demonstrate the effectiveness of our assignment technique, we conducted a numerical study and a controlled user study to compare our approach with default color assignments; our findings were verified by two expert studies. The results show that our approach is able to support users in distinguishing cluster numbers faster and more precisely than default assignment methods.

Selecting a good aspect ratio is crucial for effective 2D diagrams. There are several aspect ratio selection methods for function plots and line charts, but only few can handle general, discrete diagrams such as 2D scatter plots. However, these methods either lack a perceptual foundation or heavily rely on intermediate isoline representations, which depend on choosing the right isovalues and are time-consuming to compute. This paper introduces a general image-based approach for selecting aspect ratios for a wide variety of 2D diagrams, ranging from scatter plots and density function plots to line charts. Our approach is derived from Federer's co-area formula and a line integral representation that enable us to directly construct image-based versions of existing selection methods using density fields. In contrast to previous methods, our approach bypasses isoline computation, so it is faster to compute, while following the perceptual foundation to select aspect ratios. Furthermore, this approach is complemented by an anisotropic kernel density estimation to construct density fields, allowing us to more faithfully characterize data patterns, such as the subgroups in scatterplots or dense regions in time series. We demonstrate the effectiveness of our approach by quantitatively comparing to previous methods and revisiting a prior user study. Finally, we present extensions for ROI banking, multi-scale banking, and the application to image data.

Traditional fisheye views for exploring large graphs introduce substantial distortions that often lead to a decreased readability of paths and other interesting structures. To overcome these problems, we propose a framework for structure-aware fisheye views. Using edge orientations as constraints for graph layout optimization allows us not only to reduce spatial and temporal distortions during fisheye zooms, but also to improve the readability of the graph structure. Furthermore, the framework enables us to optimize fisheye lenses towards specific tasks and design a family of new lenses: polyfocal, cluster, and path lenses. A GPU implementation lets us process large graphs with up to 15,000 nodes at interactive rates. A comprehensive evaluation, a user study, and two case studies demonstrate that our structure-aware fisheye views improve layout readability and user performance.

Fuzzy clustering assigns a probability of membership for a datum to a cluster, which veritably reflects real-world clustering scenarios but significantly increases the complexity of understanding fuzzy clusters. Many studies have demonstrated that visualization techniques for multi-dimensional data are beneficial to understand fuzzy clusters. However, no empirical evidence exists on the effectiveness and efficiency of these visualization techniques in solving analytical tasks featured by fuzzy clusters. In this paper, we conduct a controlled experiment to evaluate the ability of fuzzy clusters analysis to use four multi-dimensional visualization techniques, namely, parallel coordinate plot, scatterplot matrix, principal component analysis, and Radviz. First, we define the analytical tasks and their representative questions specific to fuzzy clusters analysis. Then, we design objective questionnaires to compare the accuracy, time, and satisfaction in using the four techniques to solve the questions. We also design subjective questionnaires to collect the experience of the volunteers with the four techniques in terms of ease of use, informativeness, and helpfulness. With a complete experiment process and a detailed result analysis, we test against four hypotheses that are formulated on the basis of our experience, and provide instructive guidance for analysts in selecting appropriate and efficient visualization techniques to analyze fuzzy clusters.

Effective exploration of spatiotemporal volumetric data sets remains a key challenge in scientific visualization. Although great advances have been made over the years, existing solutions typically focus on only one or two aspects of data analysis and visualization. A streamlined workflow for analyzing time-varying data in a comprehensive and unified manner is still missing. Towards this goal, we present a novel approach for time-varying data visualization that encompasses keyframe identification, feature extraction and tracking under a single, unified framework. At the heart of our approach lies in the GPU-accelerated BlockMatch method, a dense block correspondence technique that extends the PatchMatch method from 2D pixels to 3D voxels. Based on the results of dense correspondence, we are able to identify keyframes from the time sequence using k-medoids clustering along with a bidirectional similarity measure. Furthermore, in conjunction with the graph cut algorithm, this framework enables us to perform fine-grained feature extraction and tracking. We tested our approach using several time-varying data sets to demonstrate its effectiveness and utility.

Deep Neural Networks (DNNs) have recently shown state of the art performance on semantic segmentation tasks, however, they still suffer from problems of poor boundary localization and spatial fragmented predictions. The difficulties lie in the requirement of making dense predictions from a long path model all at once since details are hard to keep when data goes through deeper layers. Instead, in this work, we decompose this difficult task into two relative simple sub-tasks: seed detection which is required to predict initial predictions without the need of wholeness and preciseness, and similarity estimation which measures the possibility of any two nodes belong to the same class without the need of knowing which class they are. We use one branch network for one sub-task each, and apply a cascade of random walks base on hierarchical semantics to approximate a complex diffusion process which propagates seed information to the whole image according to the estimated similarities. The proposed DifNet consistently produces improvements over the baseline models with the same depth and with the equivalent number of parameters, and also achieves promising performance on Pascal VOC and Pascal Context dataset. OurDifNet is trained end-to-end without complex loss functions.

Abstract The symmetrizable and converged Laplace–Beltrami operator ( ) is an indispensable tool for spectral geometrical analysis of point clouds. The , introduced by Liu et al. [LPG12] is guaranteed to be symmetrizable, but its convergence degrades when it is applied to models with sharp features. In this paper, we propose a novel , which is not only symmetrizable but also can handle the point‐sampled surface containing significant sharp features. By constructing the anisotropic Voronoi diagram in the local tangential space, the can be well constructed for any given point. To compute the area of anisotropic Voronoi cell, we introduce an efficient approximation by projecting the cell to the local tangent plane and have proved its convergence. We present numerical experiments that clearly demonstrate the robustness and efficiency of the proposed for point clouds that may contain noise, outliers, and non‐uniformities in thickness and spacing. Moreover, we can show that its spectrum is more accurate than the ones from existing for scan points or surfaces with sharp features.

We present EdWordle, a method for consistently editing word clouds. At its heart, EdWordle allows users to move and edit words while preserving the neighborhoods of other words. To do so, we combine a constrained rigid body simulation with a neighborhood-aware local Wordle algorithm to update the cloud and to create very compact layouts. The consistent and stable behavior of EdWordle enables users to create new forms of word clouds such as storytelling clouds in which the position of words is carefully edited. We compare our approach with state-of-the-art methods and show that we can improve user performance, user satisfaction, as well as the layout itself.

Dimensionality reduction (DR) is a common strategy for visual analysis of labeled high-dimensional data. Low-dimensional representations of the data help, for instance, to explore the class separability and the spatial distribution of the data. Widely-used unsupervised DR methods like PCA do not aim to maximize the class separation, while supervised DR methods like LDA often assume certain spatial distributions and do not take perceptual capabilities of humans into account. These issues make them ineffective for complicated class structures. Towards filling this gap, we present a perception-driven linear dimensionality reduction approach that maximizes the perceived class separation in projections. Our approach builds on recent developments in perception-based separation measures that have achieved good results in imitating human perception. We extend these measures to be density-aware and incorporate them into a customized simulated annealing algorithm, which can rapidly generate a near optimal DR projection. We demonstrate the effectiveness of our approach by comparing it to state-of-the-art DR methods on 93 datasets, using both quantitative measure and human judgments. We also provide case studies with class-imbalanced and unlabeled data.

Line graphs are usually considered to be the best choice for visualizing time series data, whereas sometimes also scatter plots are used for showing main trends. So far there are no guidelines that indicate which of these visualization methods better display trends in time series for a given canvas. Assuming that the main information in a time series is its overall trend, we propose an algorithm that automatically picks the visualization method that reveals this trend best. This is achieved by measuring the visual consistency between the trend curve represented by a LOESS fit and the trend described by a scatter plot or a line graph. To measure the consistency between our algorithm and user choices, we performed an empirical study with a series of controlled experiments that show a large correspondence. In a factor analysis we furthermore demonstrate that various visual and data factors have effects on the preference for a certain type of visualization.

We present an improved stress majorization method that incorporates various constraints, including directional constraints without the necessity of solving a constraint optimization problem. This is achieved by reformulating the stress function to impose constraints on both the edge vectors and lengths instead of just on the edge lengths (node distances). This is a unified framework for both constrained and unconstrained graph visualizations, where we can model most existing layout constraints, as well as develop new ones such as the star shapes and cluster separation constraints within stress majorization. This improvement also allows us to parallelize computation with an efficient GPU conjugant gradient solver, which yields fast and stable solutions, even for large graphs. As a result, we allow the constraint-based exploration of large graphs with 10K nodes - an approach which previous methods cannot support.

The aspect ratio of a line chart heavily influences the perception of the underlying data. Different methods explore different criteria in choosing aspect ratios, but so far, it was still unclear how to select aspect ratios appropriately for any given data. This paper provides a guideline for the user to choose aspect ratios for any input 1D curves by conducting an in-depth analysis of aspect ratio selection methods both theoretically and experimentally. By formulating several existing methods as line integrals, we explain their parameterization invariance. Moreover, we derive a new and improved aspect ratio selection method, namely the -LOR (local orientation resolution), with a certain degree of parameterization invariance. Furthermore, we connect different methods, including AL (arc length based method), the banking to 45 principle, RV (resultant vector) and AS (average absolute slope), as well as -LOR and AO (average absolute orientation). We verify these connections by a comparative evaluation involving various data sets, and show that the selections by RV and -LOR are complementary to each other for most data. Accordingly, we propose the dual-scale banking technique that combines the strengths of RV and -LOR, and demonstrate its practicability using multiple real-world data sets.

Abstract One main task for domain experts in analysing their nD data is to detect and interpret class/cluster separations and outliers. In fact, an important question is, which features/dimensions separate classes best or allow a cluster‐based data classification. Common approaches rely on projections from nD to 2D, which comes with some challenges, such as: The space of projection contains an infinite number of items. How to find the right one? The projection approaches suffers from distortions and misleading effects. How to rely to the projected class/cluster separation? The projections involve the complete set of dimensions/features. How to identify irrelevant dimensions? Thus, to address these challenges, we introduce a visual analytics concept for the feature selection based on linear discriminative star coordinates (DSC), which generate optimal cluster separating views in a linear sense for both labeled and unlabeled data. This way the user is able to explore how each dimension contributes to clustering. To support to explore relations between clusters and data dimensions, we provide a set of cluster‐aware interactions allowing to smartly iterate through subspaces of both records and features in a guided manner. We demonstrate our features selection approach for optimal cluster/class separation analysis with a couple of experiments on real‐life benchmark high‐dimensional data sets.

The aspect ratio of a plot can strongly influence the perception of trends in the data. Arc length based aspect ratio selection (AL) has demonstrated many empirical advantages over previous methods. However, it is still not clear why and when this method works. In this paper, we attempt to unravel its mystery by exploring its mathematical foundation. First, we explain the rationale why this method is parameterization invariant and follow the same rationale to extend previous methods which are not parameterization invariant. As such, we propose maximizing weighted local curvature (MLC), a parameterization invariant form of local orientation resolution (LOR) and reveal the theoretical connection between average slope (AS) and resultant vector (RV). Furthermore, we establish a mathematical connection between AL and banking to 45 degrees and derive the upper and lower bounds of its average absolute slopes. Finally, we conduct a quantitative comparison that revises the understanding of aspect ratio selection methods in three aspects: (1) showing that AL, AWO and RV always perform very similarly while MS is not; (2) demonstrating the advantages in the robustness of RV over AL; (3) providing a counterexample where all previous methods produce poor results while MLC works well.

Searching the k-nearest matching patches for each patch in an input image, i.e., computing the k-nearest-neighbor fields ($k$-NNF), is a core part of various computer vision/graphics algorithms. In this paper, we show that $k$-NNF can be efficiently computed using a novel artificial multi-bee-colony (AMBC) algorithm, where each patch uses a dedicated bee colony to search for its k-nearest matches. As a population-based algorithm, AMBC is capable of escaping local optima. The added communication among different colonies further allows good matches to be quickly propagated across the image. In addition, AMBC makes no assumption about the neighborhood structure or communication direction, making it directly applicable to image sets and suitable for parallel processing. Quantitative evaluations show that AMBC can find solutions that are much closer to the ground truth than the generalized PatchMatch algorithm does. It also outperforms the PatchMatch Graph over image sets.

Abstract We present a distillation algorithm which operates on a large, unstructured, and noisy collection of internet images returned from an online object query. We introduce the notion of a distilled set, which is a clean, coherent, and structured subset of inlier images. In addition, the object of interest is properly segmented out throughout the distilled set. Our approach is unsupervised, built on a novel clustering scheme, and solves the distillation and object segmentation problems simultaneously. In essence, instead of distilling the collection of images, we distill a collection of loosely cutout foreground “shapes”, which may or may not contain the queried object. Our key observation, which motivated our clustering scheme, is that outlier shapes are expected to be random in nature, whereas, inlier shapes, which do tightly enclose the object of interest, tend to be well supported by similar shapes captured in similar views. We analyze the commonalities among candidate foreground segments, without aiming to analyze their semantics, but simply by clustering similar shapes and considering only the most significant clusters representing non‐trivial shapes. We show that when tuned conservatively, our distillation algorithm is able to extract a near perfect subset of true inliers. Furthermore, we show that our technique scales well in the sense that the precision rate remains high, as the collection grows. We demonstrate the utility of our distillation results with a number of interesting graphics applications.

Abstract Precipitation forecast verification is essential to the quality of a forecast. The Gaussian mixture model (GMM) can be used to approximate the precipitation of several rain bands and provide a concise view of the data, which is especially useful for comparing forecast and observation data. The robustness of such comparison mainly depends on the consistency of and the correspondence between the extracted rain bands in the forecast and observation data. We propose a novel co‐estimation approach based on GMM in which forecast and observation data are analysed simultaneously. This approach naturally increases the consistency of and correspondence between the extracted rain bands by exploiting the similarity between both forecast and observation data. Moreover, a novel visualization and exploration framework is implemented to help the meteorologists gain insight from the forecast. The proposed approach was applied to the forecast and observation data provided by the China Meteorological Administration. The results are evaluated by meteorologists and novel insight has been gained.

We introduce projective analysis for semantic segmentation and labeling of 3D shapes. The analysis treats an input 3D shape as a collection of 2D projections, labels each projection by transferring knowledge from existing labeled images, and back-projects and fuses the labelings on the 3D shape. The image-space analysis involves matching projected binary images of 3D objects based on a novel bi-class Hausdorff distance . The distance is topology-aware by accounting for internal holes in the 2D figures and it is applied to piecewise-linearly warped object projections to compensate for part scaling and view discrepancies. Projective analysis simplifies the processing task by working in a lower-dimensional space, circumvents the requirement of having complete and well-modeled 3D shapes, and addresses the data challenge for 3D shape analysis by leveraging the massive available image data. A large and dense labeled set ensures that the labeling of a given projected image can be inferred from closely matched labeled images. We demonstrate semantic labeling of imperfect (e.g., incomplete or self-intersecting) 3D models which would be otherwise difficult to analyze without taking the projective analysis approach.

Abstract Two‐dimensional transfer functions are an effective and well‐accepted tool in volume classification. The design of them mostly depends on the user's experience and thus remains a challenge. Therefore, we present an approach in this paper to automate the transfer function design based on 2D density plots. By exploiting their smoothness, we adopted the Morse theory to automatically decompose the feature space into a set of valley cells. We design a simplification process based on cell separability to eliminate cells which are mainly caused by noise in the original volume data. Boundary persistence is first introduced to measure the separability between adjacent cells and to suitably merge them. Afterward, a reasonable classification result is achieved where each cell represents a potential feature in the volume data. This classification procedure is automatic and facilitates an arbitrary number and shape of features in the feature space. The opacity of each feature is determined by its persistence and size. To further incorporate the user's prior knowledge, a hierarchical feature representation is created by successive merging of the cells. With this representation, the user is allowed to merge or split features of interest and set opacity and color freely. Experiments on various volumetric data sets demonstrate the effectiveness and usefulness of our approach in transfer function generation.

Unsupervised co-analysis of a set of shapes is a difficult problem since the geometry of the shapes alone cannot always fully describe the semantics of the shape parts. In this paper, we propose a semi-supervised learning method where the user actively assists in the co-analysis by iteratively providing inputs that progressively constrain the system. We introduce a novel constrained clustering method based on a spring system which embeds elements to better respect their inter-distances in feature space together with the user-given set of constraints. We also present an active learning method that suggests to the user where his input is likely to be the most effective in refining the results. We show that each single pair of constraints affects many relations across the set. Thus, the method requires only a sparse set of constraints to quickly converge toward a consistent and error-free semantic labeling of the set.

Abstract Due to 3D occlusion, the specification of proper opacities in direct volume rendering is a time‐consuming and unintuitive process. The visibility histograms introduced by Correa and Ma reflect the effect of occlusion by measuring the influence of each sample in the histogram to the rendered image. However, the visibility is defined on individual samples, while volume exploration focuses on conveying the spatial relationships between features. Moreover, the high computational cost and large memory requirement limits its application in multi‐dimensional transfer function design. In this paper, we extend visibility histograms to feature visibility, which measures the contribution of each feature in the rendered image. Compared to visibility histograms, it has two distinctive advantages for opacity specification. First, the user can directly specify the visibilities for features and the opacities are automatically generated using an optimization algorithm. Second, its calculation requires only one rendering pass with no additional memory requirement. This feature visibility based opacity specification is fast and compatible with all types of transfer function design. Furthermore, we introduce a two‐step volume exploration scheme, in which an automatic optimization is first performed to provide a clear illustration of the spatial relationship and then the user adjusts the visibilities directly to achieve the desired feature enhancement. The effectiveness of this scheme is demonstrated by experimental results on several volumetric datasets.

The multidimensional transfer function is a flexible and effective tool for exploring volume data. However, designing an appropriate transfer function is a trial-and-error process and remains a challenge. In this paper, we propose a novel volume exploration scheme that explores volumetric structures in the feature space by modeling the space using the Gaussian mixture model (GMM). Our new approach has three distinctive advantages. First, an initial feature separation can be automatically achieved through GMM estimation. Second, the calculated Gaussians can be directly mapped to a set of elliptical transfer functions (ETFs), facilitating a fast pre-integrated volume rendering process. Third, an inexperienced user can flexibly manipulate the ETFs with the assistance of a suite of simple widgets, and discover potential features with several interactions. We further extend the GMM-based exploration scheme to time-varying data sets using an incremental GMM estimation algorithm. The algorithm estimates the GMM for one time step by using itself and the GMM generated from its previous steps. Sequentially applying the incremental algorithm to all time steps in a selected time interval yields a preliminary classification for each time step. In addition, the computed ETFs can be freely adjusted. The adjustments are then automatically propagated to other time steps. In this way, coherent user-guided exploration of a given time interval is achieved. Our GPU implementation demonstrates interactive performance and good scalability. The effectiveness of our approach is verified on several data sets.

This paper presents an interactive transfer function design tool based on ellipsoidal Gaussian transfer functions (ETFs). Our approach explores volumetric features in the statistical space by modeling the space using the Gaussian mixture model (GMM) with a small number of Gaussians to maximize the likelihood of feature separation. Instant visual feedback is possible by mapping these Gaussians to ETFs and analytically integrating these ETFs in the context of the pre-integrated volume rendering process. A suite of intuitive control widgets is designed to offer automatic transfer function generation and flexible manipulations, allowing an inexperienced user to easily explore undiscovered features with several simple interactions. Our GPU implementation demonstrates interactive performance and plausible scalability which compare favorably with existing solutions. The effectiveness of our approach has been verified on several datasets.