Uncertainty-Aware Multidimensional Ensemble Data Visualization and Exploration

Fuzzy Spreadsheet: Understanding and Exploring Uncertainties in Tabular Calculations

Spreadsheet-based tools provide a simple yet effective way of calculating values, which makes them the number-one choice for building and formalizing simple models for budget planning and many other applications. A cell in a spreadsheet holds one specific value and gives a discrete, overprecise view of the underlying model. Therefore, spreadsheets are of limited use when investigating the inherent uncertainties of such models and answering what-if questions. Existing extensions typically require a complex modeling process that cannot easily be embedded in a tabular layout. In Fuzzy Spreadsheet, a cell can hold and display a distribution of values. This integrated uncertainty-handling immediately conveys sensitivity and robustness information. The fuzzification of the cells enables calculations not only with precise values but also with distributions, and probabilities. We conservatively added and carefully crafted visuals to maintain the look and feel of a traditional spreadsheet while facilitating what-if analyses. Given a user-specified reference cell, Fuzzy Spreadsheet automatically extracts and visualizes contextually relevant information, such as impact, uncertainty, and degree of neighborhood, for the selected and related cells. To evaluate its usability and the perceived mental effort required, we conducted a user study. The results show that our approach outperforms traditional spreadsheets in terms of answer correctness, response time, and perceived mental effort in almost all tasks tested.

VDL-Surrogate: A View-Dependent Latent-based Model for Parameter Space Exploration of Ensemble Simulations

We propose VDL-Surrogate, a view-dependent neural-network-latent-based surrogate model for parameter space exploration of ensemble simulations that allows high-resolution visualizations and user-specified visual mappings. Surrogate-enabled parameter space exploration allows domain scientists to preview simulation results without having to run a large number of computationally costly simulations. Limited by computational resources, however, existing surrogate models may not produce previews with sufficient resolution for visualization and analysis. To improve the efficient use of computational resources and support high-resolution exploration, we perform ray casting from different viewpoints to collect samples and produce compact latent representations. This latent encoding process reduces the cost of surrogate model training while maintaining the output quality. In the model training stage, we select viewpoints to cover the whole viewing sphere and train corresponding VDL-Surrogate models for the selected viewpoints. In the model inference stage, we predict the latent representations at previously selected viewpoints and decode the latent representations to data space. For any given viewpoint, we make interpolations over decoded data at selected viewpoints and generate visualizations with user-specified visual mappings. We show the effectiveness and efficiency of VDL-Surrogate in cosmological and ocean simulations with quantitative and qualitative evaluations. Source code is publicly available at https://github.com/trainsn/VDL-Surrogate.

Visualizing Ensemble Predictions of Music Mood

Music mood classification has been a challenging problem in comparison with other music classification problems (e.g., genre, composer, or period). One solution for addressing this challenge is to use an ensemble of machine learning models. In this paper, we show that visualization techniques can effectively convey the popular prediction as well as uncertainty at different music sections along the temporal axis while enabling the analysis of individual ML models in conjunction with their application to different musical data. In addition to the traditional visual designs, such as stacked line graph, ThemeRiver, and pixel-based visualization, we introduce a new variant of ThemeRiver, called "dual-flux ThemeRiver", which allows viewers to observe and measure the most popular prediction more easily than stacked line graph and ThemeRiver. Together with pixel-based visualization, dual-flux ThemeRiver plots can also assist in model-development workflows, in addition to annotating music using ensemble model predictions.

Uncertainty-Aware Multidimensional Scaling

We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty. With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.

Development and Evaluation of Two Approaches of Visual Sensitivity Analysis to Support Epidemiological Modeling

Computational modeling is a commonly used technology in many scientific disciplines and has played a noticeable role in combating the COVID-19 pandemic. Modeling scientists conduct sensitivity analysis frequently to observe and monitor the behavior of a model during its development and deployment. The traditional algorithmic ranking of sensitivity of different parameters usually does not provide modeling scientists with sufficient information to understand the interactions between different parameters and model outputs, while modeling scientists need to observe a large number of model runs in order to gain actionable information for parameter optimization. To address the above challenge, we developed and compared two visual analytics approaches, namely: algorithm-centric and visualization-assisted, and visualization-centric and algorithm-assisted. We evaluated the two approaches based on a structured analysis of different tasks in visual sensitivity analysis as well as the feedback of domain experts. While the work was carried out in the context of epidemiological modeling, the two approaches developed in this work are directly applicable to a variety of modeling processes featuring time series outputs, and can be extended to work with models with other types of outputs.

Simulation-Based Optimization: Implications of Complex Adaptive Systems and Deep Uncertainty

Within the modeling and simulation community, simulation-based optimization has often been successfully used to improve productivity and business processes. However, the increased importance of using simulation to better understand complex adaptive systems and address operations research questions characterized by deep uncertainty, such as the need for policy support within socio-technical systems, leads to the necessity to revisit the way simulation can be applied in this new area. Similar observations can be made for complex adaptive systems that constantly change their behavior, which is reflected in a continually changing solution space. Deep uncertainty describes problems with inadequate or incomplete information about the system and the outcomes of interest. Complex adaptive systems under deep uncertainty must integrate the search for robust solutions by conducting exploratory modeling and analysis. This article visits both domains, shows what the new challenges are, and provides a framework to apply methods from operational research and complexity science to address them. With such extensions, simulation-based approaches will be able to support these new areas as well, although optimal solutions may no longer be obtainable. Instead, robust and sufficient solutions will become the objective of optimization processes.

GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations

We propose GNN-Surrogate, a graph neural network-based surrogate model to explore the parameter space of ocean climate simulations. Parameter space exploration is important for domain scientists to understand the influence of input parameters (e.g., wind stress) on the simulation output (e.g., temperature). The exploration requires scientists to exhaust the complicated parameter space by running a batch of computationally expensive simulations. Our approach improves the efficiency of parameter space exploration with a surrogate model that predicts the simulation outputs accurately and efficiently. Specifically, GNN-Surrogate predicts the output field with given simulation parameters so scientists can explore the simulation parameter space with visualizations from user-specified visual mappings. Moreover, our graph-based techniques are designed for unstructured meshes, making the exploration of simulation outputs on irregular grids efficient. For efficient training, we generate hierarchical graphs and use adaptive resolutions. We give quantitative and qualitative evaluations on the MPAS-Ocean simulation to demonstrate the effectiveness and efficiency of GNN-Surrogate. Source code is publicly available at https://github.com/trainsn/GNN-Surrogate.

Visual Parameter Space Analysis for Optimizing the Quality of Industrial Nonwovens

Technical textiles, in particular, nonwovens used, for example, in medical masks, have become increasingly important in our daily lives. The quality of these textiles depends on the manufacturing process parameters that cannot be easily optimized in live settings. In this article, we present a visual analytics framework that enables interactive parameter space exploration and parameter optimization in industrial production processes of nonwovens. Therefore, we survey analysis strategies used in optimizing industrial production processes of nonwovens and support them in our tool. To enable real-time interaction, we augment the digital twin with a machine learning surrogate model for rapid quality computations. In addition, we integrate mechanisms for sensitivity analysis that ensure consistent product quality under mild parameter changes. In our case study, we explore the finding of optimal parameter sets, investigate the input-output relationship between parameters, and conduct a sensitivity analysis to find settings that result in robust quality.

Uncertainty-Oriented Ensemble Data Visualization and Exploration using Variable Spatial Spreading

As an important method of handling potential uncertainties in numerical simulations, ensemble simulation has been widely applied in many disciplines. Visualization is a promising and powerful ensemble simulation analysis method. However, conventional visualization methods mainly aim at data simplification and highlighting important information based on domain expertise instead of providing a flexible data exploration and intervention mechanism. Trial-and-error procedures have to be repeatedly conducted by such approaches. To resolve this issue, we propose a new perspective of ensemble data analysis using the attribute variable dimension as the primary analysis dimension. Particularly, we propose a variable uncertainty calculation method based on variable spatial spreading. Based on this method, we design an interactive ensemble analysis framework that provides a flexible interactive exploration of the ensemble data. Particularly, the proposed spreading curve view, the region stability heat map view, and the temporal analysis view, together with the commonly used 2D map view, jointly support uncertainty distribution perception, region selection, and temporal analysis, as well as other analysis requirements. We verify our approach by analyzing a real-world ensemble simulation dataset. Feedback collected from domain experts confirms the efficacy of our framework.

InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations

We propose InSituNet, a deep learning based surrogate model to support parameter space exploration for ensemble simulations that are visualized in situ. In situ visualization, generating visualizations at simulation time, is becoming prevalent in handling large-scale simulations because of the I/O and storage constraints. However, in situ visualization approaches limit the flexibility of post-hoc exploration because the raw simulation data are no longer available. Although multiple image-based approaches have been proposed to mitigate this limitation, those approaches lack the ability to explore the simulation parameters. Our approach allows flexible exploration of parameter space for large-scale ensemble simulations by taking advantage of the recent advances in deep learning. Specifically, we design InSituNet as a convolutional regression model to learn the mapping from the simulation and visualization parameters to the visualization results. With the trained model, users can generate new images for different simulation parameters under various visualization settings, which enables in-depth analysis of the underlying ensemble simulations. We demonstrate the effectiveness of InSituNet in combustion, cosmology, and ocean simulations through quantitative and qualitative evaluations.

Visualization and Visual Analysis of Ensemble Data: A Survey

Over the last decade, ensemble visualization has witnessed a significant development due to the wide availability of ensemble data, and the increasing visualization needs from a variety of disciplines. From the data analysis point of view, it can be observed that many ensemble visualization works focus on the same facet of ensemble data, use similar data aggregation or uncertainty modeling methods. However, the lack of reflections on those essential commonalities and a systematic overview of those works prevents visualization researchers from effectively identifying new or unsolved problems and planning for further developments. In this paper, we take a holistic perspective and provide a survey of ensemble visualization. Specifically, we study ensemble visualization works in the recent decade, and categorize them from two perspectives: (1) their proposed visualization techniques; and (2) their involved analytic tasks. For the first perspective, we focus on elaborating how conventional visualization techniques (e.g., surface, volume visualization techniques) have been adapted to ensemble data; for the second perspective, we emphasize how analytic tasks (e.g., comparison, clustering) have been performed differently for ensemble data. From the study of ensemble visualization literature, we have also identified several research trends, as well as some future research opportunities.

Multidimensional Projection for Visual Analytics: Linking Techniques with Distortions, Tasks, and Layout Enrichment

Visual analysis of multidimensional data requires expressive and effective ways to reduce data dimensionality to encode them visually. Multidimensional projections (MDP) figure among the most important visualization techniques in this context, transforming multidimensional data into scatter plots whose visual patterns reflect some notion of similarity in the original data. However, MDP come with distortions that make these visual patterns not trustworthy, hindering users to infer actual data characteristics. Moreover, the patterns present in the scatter plots might not be enough to allow a clear understanding of multidimensional data, motivating the development of layout enrichment methodologies to operate together with MDP. This survey attempts to cover the main aspects of MDP as a visualization and visual analytic tool. It provides detailed analysis and taxonomies as to the organization of MDP techniques according to their main properties and traits, discussing the impact of such properties for visual perception and other human factors. The survey also approaches the different types of distortions that can result from MDP mappings and it overviews existing mechanisms to quantitatively evaluate such distortions. A qualitative analysis of the impact of distortions on the different analytic tasks performed by users when exploring multidimensional data through MDP is also presented. Guidelines for choosing the best MDP for an intended task are also provided as a result of this analysis. Finally, layout enrichment schemes to debunk MDP distortions and/or reveal relevant information not directly inferable from the scatter plot are reviewed and discussed in the light of new taxonomies. We conclude the survey providing future research axes to fill discovered gaps in this domain.

A Semantic-Based Method for Visualizing Large Image Collections

Interactive visualization of large image collections is important and useful in many applications, such as personal album management and user profiling on images. However, most prior studies focus on using low-level visual features of images, such as texture and color histogram, to create visualizations without considering the more important semantic information embedded in images. This paper proposes a novel visual analytic system to analyze images in a semantic-aware manner. The system mainly comprises two components: a semantic information extractor and a visual layout generator. The semantic information extractor employs an image captioning technique based on convolutional neural network (CNN) to produce descriptive captions for images, which can be transformed into semantic keywords. The layout generator employs a novel co-embedding model to project images and the associated semantic keywords to the same 2D space. Inspired by the galaxy metaphor, we further turn the projected 2D space to a galaxy visualization of images, in which semantic keywords and images are visually encoded as stars and planets. Our system naturally supports multi-scale visualization and navigation, in which users can immediately see a semantic overview of an image collection and drill down for detailed inspection of a certain group of images. Users can iteratively refine the visual layout by integrating their domain knowledge into the co-embedding process. Two task-based evaluations are conducted to demonstrate the effectiveness of our system.

Visual Analytics of Heterogeneous Data Using Hypergraph Learning

For real-world learning tasks (e.g., classification), graph-based models are commonly used to fuse the information distributed in diverse data sources, which can be heterogeneous, redundant, and incomplete. These models represent the relations in different datasets as pairwise links. However, these links cannot deal with high-order relations which connect multiple objects (e.g., in public health datasets, more than two patient groups admitted by the same hospital in 2014). In this article, we propose a visual analytics approach for the classification on heterogeneous datasets using the hypergraph model. The hypergraph is an extension to traditional graphs in which a hyperedge connects multiple vertices instead of just two. We model various high-order relations in heterogeneous datasets as hyperedges and fuse different datasets with a unified hypergraph structure. We use the hypergraph learning algorithm for predicting missing labels in the datasets. To allow users to inject their domain knowledge into the model-learning process, we augment the traditional learning algorithm in a number of ways. In addition, we also propose a set of visualizations which enable the user to construct the hypergraph structure and the parameters of the learning model interactively during the analysis. We demonstrate the capability of our approach via two real-world cases.

EnsembleLens: Ensemble-based Visual Exploration of Anomaly Detection Algorithms with Multidimensional Data

The results of anomaly detection are sensitive to the choice of detection algorithms as they are specialized for different properties of data, especially for multidimensional data. Thus, it is vital to select the algorithm appropriately. To systematically select the algorithms, ensemble analysis techniques have been developed to support the assembly and comparison of heterogeneous algorithms. However, challenges remain due to the absence of the ground truth, interpretation, or evaluation of these anomaly detectors. In this paper, we present a visual analytics system named EnsembleLens that evaluates anomaly detection algorithms based on the ensemble analysis process. The system visualizes the ensemble processes and results by a set of novel visual designs and multiple coordinated contextual views to meet the requirements of correlation analysis, assessment and reasoning of anomaly detection algorithms. We also introduce an interactive analysis workflow that dynamically produces contextualized and interpretable data summaries that allow further refinements of exploration results based on user feedback. We demonstrate the effectiveness of EnsembleLens through a quantitative evaluation, three case studies with real-world data and interviews with two domain experts.

Visualizing High-Dimensional Data: Advances in the Past Decade

Massive simulations and arrays of sensing devices, in combination with increasing computing resources, have generated large, complex, high-dimensional datasets used to study phenomena across numerous fields of study. Visualization plays an important role in exploring such datasets. We provide a comprehensive survey of advances in high-dimensional data visualization that focuses on the past decade. We aim at providing guidance for data practitioners to navigate through a modular view of the recent advances, inspiring the creation of new visualizations along the enriched visualization pipeline, and identifying future opportunities for visualization research.

Multi-Resolution Climate Ensemble Parameter Analysis with Nested Parallel Coordinates Plots

Due to the uncertain nature of weather prediction, climate simulations are usually performed multiple times with different spatial resolutions. The outputs of simulations are multi-resolution spatial temporal ensembles. Each simulation run uses a unique set of values for multiple convective parameters. Distinct parameter settings from different simulation runs in different resolutions constitute a multi-resolution high-dimensional parameter space. Understanding the correlation between the different convective parameters, and establishing a connection between the parameter settings and the ensemble outputs are crucial to domain scientists. The multi-resolution high-dimensional parameter space, however, presents a unique challenge to the existing correlation visualization techniques. We present Nested Parallel Coordinates Plot (NPCP), a new type of parallel coordinates plots that enables visualization of intra-resolution and inter-resolution parameter correlations. With flexible user control, NPCP integrates superimposition, juxtaposition and explicit encodings in a single view for comparative data visualization and analysis. We develop an integrated visual analytics system to help domain scientists understand the connection between multi-resolution convective parameters and the large spatial temporal ensembles. Our system presents intricate climate ensembles with a comprehensive overview and on-demand geographic details. We demonstrate NPCP, along with the climate ensemble visualization system, based on real-world use-cases from our collaborators in computational and predictive science.

An Uncertainty-Aware Approach for Exploratory Microblog Retrieval

Although there has been a great deal of interest in analyzing customer opinions and breaking news in microblogs, progress has been hampered by the lack of an effective mechanism to discover and retrieve data of interest from microblogs. To address this problem, we have developed an uncertainty-aware visual analytics approach to retrieve salient posts, users, and hashtags. We extend an existing ranking technique to compute a multifaceted retrieval result: the mutual reinforcement rank of a graph node, the uncertainty of each rank, and the propagation of uncertainty among different graph nodes. To illustrate the three facets, we have also designed a composite visualization with three visual components: a graph visualization, an uncertainty glyph, and a flow map. The graph visualization with glyphs, the flow map, and the uncertainty analysis together enable analysts to effectively find the most uncertain results and interactively refine them. We have applied our approach to several Twitter datasets. Qualitative evaluation and two real-world case studies demonstrate the promise of our approach for retrieving high-quality microblog data.