An information-aware framework for exploring multivariate data sets

A Survey of Designs for Combined 2D+3D Visual Representations

We examine visual representations of data that make use of combinations of both 2D and 3D data mappings. Combining 2D and 3D representations is a common technique that allows viewers to understand multiple facets of the data with which they are interacting. While 3D representations focus on the spatial character of the data or the dedicated 3D data mapping, 2D representations often show abstract data properties and take advantage of the unique benefits of mapping to a plane. Many systems have used unique combinations of both types of data mappings effectively. Yet there are no systematic reviews of the methods in linking 2D and 3D representations. We systematically survey the relationships between 2D and 3D visual representations in major visualization publications-IEEE VIS, IEEE TVCG, and EuroVis-from 2012 to 2022. We closely examined 105 articles where 2D and 3D representations are connected visually, interactively, or through animation. These approaches are designed based on their visual environment, the relationships between their visual representations, and their possible layouts. Through our analysis, we introduce a design space as well as provide design guidelines for effectively linking 2D and 3D visual representations.

Interactive polar diagrams for model comparison

OBJECTIVE

Evaluating the performance of multiple complex models, such as those found in biology, medicine, climatology, and machine learning, using conventional approaches is often challenging when using various evaluation metrics simultaneously. The traditional approach, which relies on presenting multi-model evaluation scores in the table, presents an obstacle when determining the similarities between the models and the order of performance.

METHODS

By combining statistics, information theory, and data visualization, juxtaposed Taylor and Mutual Information Diagrams permit users to track and summarize the performance of one model or a collection of different models. To uncover linear and nonlinear relationships between models, users may visualize one or both charts.

RESULTS

Our library presents the first publicly available implementation of the Mutual Information Diagram and its new interactive capabilities, as well as the first publicly available implementation of an interactive Taylor Diagram. Extensions have been implemented so that both diagrams can display temporality, multimodality, and multivariate data sets, and feature one scalar model property such as uncertainty. Our library, named polar-diagrams, supports both continuous and categorical attributes.

CONCLUSION

The library can be used to quickly and easily assess the performances of complex models, such as those found in machine learning, climate, or biomedical domains.

voxel2vec: A Natural Language Processing Approach to Learning Distributed Representations for Scientific Data

Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and ensemble data, are intricate and complex. This paper presents voxel2vec, a novel unsupervised representation learning model, which is used to learn distributed representations of scalar values/scalar-value combinations in a low-dimensional vector space. Its basic assumption is that if two scalar values/scalar-value combinations have similar contexts, they usually have high similarity in terms of features. By representing scalar values/scalar-value combinations as symbols, voxel2vec learns the similarity between them in the context of spatial distribution and then allows us to explore the overall association between volumes by transfer prediction. We demonstrate the usefulness and effectiveness of voxel2vec by comparing it with the isosurface similarity map of univariate data and applying the learned distributed representations to feature classification for multivariate data and to association analysis for time-varying and ensemble data.

A Bounded Measure for Estimating the Benefit of Visualization (Part I): Theoretical Discourse and Conceptual Evaluation

Information theory can be used to analyze the cost–benefit of visualization processes. However, the current measure of benefit contains an unbounded term that is neither easy to estimate nor intuitive to interpret. In this work, we propose to revise the existing cost–benefit measure by replacing the unbounded term with a bounded one. We examine a number of bounded measures that include the Jenson–Shannon divergence, its square root, and a new divergence measure formulated as part of this work. We describe the rationale for proposing a new divergence measure. In the first part of this paper, we focus on the conceptual analysis of the mathematical properties of these candidate measures. We use visualization to support the multi-criteria comparison, narrowing the search down to several options with better mathematical properties. The theoretical discourse and conceptual evaluation in this part provides the basis for further data-driven evaluation based on synthetic and experimental case studies that are reported in the second part of this paper.

Probabilistic Data-Driven Sampling via Multi-Criteria Importance Analysis

Although supercomputers are becoming increasingly powerful, their components have thus far not scaled proportionately. Compute power is growing enormously and is enabling finely resolved simulations that produce never-before-seen features. However, I/O capabilities lag by orders of magnitude, which means only a fraction of the simulation data can be stored for post hoc analysis. Prespecified plans for saving features and quantities of interest do not work for features that have not been seen before. Data-driven intelligent sampling schemes are needed to detect and save important parts of the simulation while it is running. Here, we propose a novel sampling scheme that reduces the size of the data by orders-of-magnitude while still preserving important regions. The approach we develop selects points with unusual data values and high gradients. We demonstrate that our approach outperforms traditional sampling schemes on a number of tasks.

V2V: A Deep Learning Approach to Variable-to-Variable Selection and Translation for Multivariate Time-Varying Data

We present V2V, a novel deep learning framework, as a general-purpose solution to the variable-to-variable (V2V) selection and translation problem for multivariate time-varying data (MTVD) analysis and visualization. V2V leverages a representation learning algorithm to identify transferable variables and utilizes Kullback-Leibler divergence to determine the source and target variables. It then uses a generative adversarial network (GAN) to learn the mapping from the source variable to the target variable via the adversarial, volumetric, and feature losses. V2V takes the pairs of time steps of the source and target variable as input for training, Once trained, it can infer unseen time steps of the target variable given the corresponding time steps of the source variable. Several multivariate time-varying data sets of different characteristics are used to demonstrate the effectiveness of V2V, both quantitatively and qualitatively. We compare V2V against histogram matching and two other deep learning solutions (Pix2Pix and CycleGAN).

Graphs from Features: Tree-Based Graph Layout for Feature Analysis

Feature Analysis has become a very critical task in data analysis and visualization. Graph structures are very flexible in terms of representation and may encode important information on features but are challenging in regards to layout being adequate for analysis tasks. In this study, we propose and develop similarity-based graph layouts with the purpose of locating relevant patterns in sets of features, thus supporting feature analysis and selection. We apply a tree layout in the first step of the strategy, to accomplish node placement and overview based on feature similarity. By drawing the remainder of the graph edges on demand, further grouping and relationships among features are revealed. We evaluate those groups and relationships in terms of their effectiveness in exploring feature sets for data analysis. Correlation of features with a target categorical attribute and feature ranking are added to support the task. Multidimensional projections are employed to plot the dataset based on selected attributes to reveal the effectiveness of the feature set. Our results have shown that the tree-graph layout framework allows for a number of observations that are very important in user-centric feature selection, and not easy to observe by any other available tool. They provide a way of finding relevant and irrelevant features, spurious sets of noisy features, groups of similar features, and opposite features, all of which are essential tasks in different scenarios of data analysis. Case studies in application areas centered on documents, images and sound data demonstrate the ability of the framework to quickly reach a satisfactory compact representation from a larger feature set.

TSR-TVD: Temporal Super-Resolution for Time-Varying Data Analysis and Visualization

We present TSR-TVD, a novel deep learning framework that generates temporal super-resolution (TSR) of time-varying data (TVD) using adversarial learning. TSR-TVD is the first work that applies the recurrent generative network (RGN), a combination of the recurrent neural network (RNN) and generative adversarial network (GAN), to generate temporal high-resolution volume sequences from low-resolution ones. The design of TSR-TVD includes a generator and a discriminator. The generator takes a pair of volumes as input and outputs the synthesized intermediate volume sequence through forward and backward predictions. The discriminator takes the synthesized intermediate volumes as input and produces a score indicating the realness of the volumes. Our method handles multivariate data as well where the trained network from one variable is applied to generate TSR for another variable. To demonstrate the effectiveness of TSR-TVD, we show quantitative and qualitative results with several time-varying multivariate data sets and compare our method against standard linear interpolation and solutions solely based on RNN or CNN.

Multivariate Pointwise Information-Driven Data Sampling and Visualization

With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large-scale multivariate spatiotemporal data sets while preserving the important data properties so that the reduced data can answer domain-specific queries involving multiple variables with sufficient accuracy. While analyzing complex scientific events, domain experts often analyze and visualize two or more variables together to obtain a better understanding of the characteristics of the data features. Therefore, data summarization techniques are required to analyze multi-variable relationships in detail and then perform data reduction such that the important features involving multiple variables are preserved in the reduced data. To achieve this, in this work, we propose a data sub-sampling algorithm for performing statistical data summarization that leverages pointwise information theoretic measures to quantify the statistical association of data points considering multiple variables and generates a sub-sampled data that preserves the statistical association among multi-variables. Using such reduced sampled data, we show that multivariate feature query and analysis can be done effectively. The efficacy of the proposed multivariate association driven sampling algorithm is presented by applying it on several scientific data sets.

Visual Exploration of Air Quality Data with a Time-correlation-partitioning Tree Based on Information Theory

<?tight?>Discovering the correlations among variables of air quality data is challenging, because the correlation time series are long-lasting, multi-faceted, and information-sparse. In this article, we propose a novel visual representation, called Time-correlation-partitioning (TCP) tree, that compactly characterizes correlations of multiple air quality variables and their evolutions. A TCP tree is generated by partitioning the information-theoretic correlation time series into pieces with respect to the variable hierarchy and temporal variations, and reorganizing these pieces into a hierarchically nested structure. The visual exploration of a TCP tree provides a sparse data traversal of the correlation variations and a situation-aware analysis of correlations among variables. This can help meteorologists understand the correlations among air quality variables better. We demonstrate the efficiency of our approach in a real-world air quality investigation scenario.

At a Glance: Pixel Approximate Entropy as a Measure of Line Chart Complexity

When inspecting information visualizations under time critical settings, such as emergency response or monitoring the heart rate in a surgery room, the user only has a small amount of time to view the visualization "at a glance". In these settings, it is important to provide a quantitative measure of the visualization to understand whether or not the visualization is too "complex" to accurately judge at a glance. This paper proposes Pixel Approximate Entropy (PAE), which adapts the approximate entropy statistical measure commonly used to quantify regularity and unpredictability in time-series data, as a measure of visual complexity for line charts. We show that PAE is correlated with user-perceived chart complexity, and that increased chart PAE correlates with reduced judgement accuracy. 'We also find that the correlation between PAE values and participants' judgment increases when the user has less time to examine the line charts.

Exploring Time-Varying Multivariate Volume Data Using Matrix of Isosurface Similarity Maps

We present a novel visual representation and interface named the matrix of isosurface similarity maps (MISM) for effective exploration of large time-varying multivariate volumetric data sets. MISM synthesizes three types of similarity maps (i.e., self, temporal, and variable similarity maps) to capture the essential relationships among isosurfaces of different variables and time steps. Additionally, it serves as the main visual mapping and navigation tool for examining the vast number of isosurfaces and exploring the underlying time-varying multivariate data set. We present temporal clustering, variable grouping, and interactive filtering to reduce the huge exploration space of MISM. In conjunction with the isovalue and isosurface views, MISM allows users to identify important isosurfaces or isosurface pairs and compare them over space, time, and value range. More importantly, we introduce path recommendation that suggests, animates, and compares traversal paths for effectively exploring MISM under varied criteria and at different levels-of-detail. A silhouette-based method is applied to render multiple surfaces of interest in a visually succinct manner. We demonstrate the effectiveness of our approach with case studies of several time-varying multivariate data sets and an ensemble data set, and evaluate our work with two domain experts.

Visual Analysis of Spatio-temporal Relations of Pairwise Attributes in Unsteady Flow

Despite significant advances in the analysis and visualization of unsteady flow, the interpretation of it's behavior still remains a challenge. In this work, we focus on the linear correlation and non-linear dependency of different physical attributes of unsteady flows to aid their study from a new perspective. Specifically, we extend the existing spatial correlation quantification, i.e. the Local Correlation Coefficient (LCC), to the spatio-temporal domain to study the correlation of attribute-pairs from both the Eulerian and Lagrangian views. To study the dependency among attributes, which need not be linear, we extend and compute the mutual information (MI) among attributes over time. To help visualize and interpret the derived correlation and dependency among attributes associated with a particle, we encode the correlation and dependency values on individual pathlines. Finally, to utilize the correlation and MI computation results to identify regions with interesting flow behavior, we propose a segmentation strategy of the flow domain based on the ranking of the strength of the attributes relations. We have applied our correlation and dependency metrics to a number of 2D and 3D unsteady flows with varying spatio-temporal kernel sizes to demonstrate and assess their effectiveness.

Drag and Track: A Direct Manipulation Interface for Contextualizing Data Instances within a Continuous Parameter Space

We present a direct manipulation technique that allows material scientists to interactively highlight relevant parameterized simulation instances located in dimensionally reduced spaces, enabling a user-defined understanding of a continuous parameter space. Our goals are two-fold: first, to build a user-directed intuition of dimensionally reduced data, and second, to provide a mechanism for creatively exploring parameter relationships in parameterized simulation sets, called ensembles. We start by visualizing ensemble data instances in dimensionally reduced scatter plots. To understand these abstract views, we employ user-defined virtual data instances that, through direct manipulation, search an ensemble for similar instances. Users can create multiple of these direct manipulation queries to visually annotate the spaces with sets of highlighted ensemble data instances. User-defined goals are therefore translated into custom illustrations that are projected onto the dimensionally reduced spaces. Combined forward and inverse searches of the parameter space follow naturally allowing for continuous parameter space prediction and visual query comparison in the context of an ensemble. The potential for this visualization technique is confirmed via expert user feedback for a shock physics application and synthetic model analysis.

Information Guided Exploration of Scalar Values and Isocontours in Ensemble Datasets

Uncertainty of scalar values in an ensemble dataset is often represented by the collection of their corresponding isocontours. Various techniques such as contour-boxplot, contour variability plot, glyphs and probabilistic marching-cubes have been proposed to analyze and visualize ensemble isocontours. All these techniques assume that a scalar value of interest is already known to the user. Not much work has been done in guiding users to select the scalar values for such uncertainty analysis. Moreover, analyzing and visualizing a large collection of ensemble isocontours for a selected scalar value has its own challenges. Interpreting the visualizations of such large collections of isocontours is also a difficult task. In this work, we propose a new information-theoretic approach towards addressing these issues. Using specific information measures that estimate the predictability and surprise of specific scalar values, we evaluate the overall uncertainty associated with all the scalar values in an ensemble system. This helps the scientist to understand the effects of uncertainty on different data features. To understand in finer details the contribution of individual members towards the uncertainty of the ensemble isocontours of a selected scalar value, we propose a conditional entropy based algorithm to quantify the individual contributions. This can help simplify analysis and visualization for systems with more members by identifying the members contributing the most towards overall uncertainty. We demonstrate the efficacy of our method by applying it on real-world datasets from material sciences, weather forecasting and ocean simulation experiments.

Discovering Public Health Nurse–Specific Family Home Visiting Intervention Patterns Using Visualization Techniques

Visualization is a Big Data method for detecting and validating previously unknown and hidden patterns within large data sets. This study used visualization techniques to discover and test novel patterns in public health nurse (PHN)–client–risk–intervention–outcome relationships. To understand the mechanism underlying risk reduction among high risk mothers, data representing complex social interventions were visualized in a series of three steps, and analyzed with other important contextual factors using standard descriptive and inferential statistics. Overall, client risk decreased after clients received personally tailored PHN services. Clinically important and unique PHN–client–risk–intervention–outcome patterns were discovered through pattern detection using streamgraphs, heat maps, and parallel coordinates techniques. Statistical evaluation validated that PHN intervention tailoring leads to improved client outcomes. The study demonstrates the importance of exploring data to discover ways to improve care quality and client outcomes. Further research is needed to examine additional factors that may influence PHN–client–risk–intervention–outcome patterns, and to test these methods with other data sets.

What May Visualization Processes Optimize?

In this paper, we present an abstract model of visualization and inference processes, and describe an information-theoretic measure for optimizing such processes. In order to obtain such an abstraction, we first examined six classes of workflows in data analysis and visualization, and identified four levels of typical visualization components, namely disseminative, observational, analytical and model-developmental visualization. We noticed a common phenomenon at different levels of visualization, that is, the transformation of data spaces (referred to as alphabets) usually corresponds to the reduction of maximal entropy along a workflow. Based on this observation, we establish an information-theoretic measure of cost-benefit ratio that may be used as a cost function for optimizing a data visualization process. To demonstrate the validity of this measure, we examined a number of successful visualization processes in the literature, and showed that the information-theoretic measure can mathematically explain the advantages of such processes over possible alternatives.

Association Analysis for Visual Exploration of Multivariate Scientific Data Sets

The heterogeneity and complexity of multivariate characteristics poses a unique challenge to visual exploration of multivariate scientific data sets, as it requires investigating the usually hidden associations between different variables and specific scalar values to understand the data's multi-faceted properties. In this paper, we present a novel association analysis method that guides visual exploration of scalar-level associations in the multivariate context. We model the directional interactions between scalars of different variables as information flows based on association rules. We introduce the concepts of informativeness and uniqueness to describe how information flows between scalars of different variables and how they are associated with each other in the multivariate domain. Based on scalar-level associations represented by a probabilistic association graph, we propose the Multi-Scalar Informativeness-Uniqueness (MSIU) algorithm to evaluate the informativeness and uniqueness of scalars. We present an exploration framework with multiple interactive views to explore the scalars of interest with confident associations in the multivariate spatial domain, and provide guidelines for visual exploration using our framework. We demonstrate the effectiveness and usefulness of our approach through case studies using three representative multivariate scientific data sets.

Visual Correlation Analysis of Numerical and Categorical Data on the Correlation Map

Correlation analysis can reveal the complex relationships that often exist among the variables in multivariate data. However, as the number of variables grows, it can be difficult to gain a good understanding of the correlation landscape and important intricate relationships might be missed. We previously introduced a technique that arranged the variables into a 2D layout, encoding their pairwise correlations. We then used this layout as a network for the interactive ordering of axes in parallel coordinate displays. Our current work expresses the layout as a correlation map and employs it for visual correlation analysis. In contrast to matrix displays where correlations are indicated at intersections of rows and columns, our map conveys correlations by spatial proximity which is more direct and more focused on the variables in play. We make the following new contributions, some unique to our map: (1) we devise mechanisms that handle both categorical and numerical variables within a unified framework, (2) we achieve scalability for large numbers of variables via a multi-scale semantic zooming approach, (3) we provide interactive techniques for exploring the impact of value bracketing on correlations, and (4) we visualize data relations within the sub-spaces spanned by correlated variables by projecting the data into a corresponding tessellation of the map.

FLDA: Latent Dirichlet Allocation Based Unsteady Flow Analysis

In this paper, we present a novel feature extraction approach called FLDA for unsteady flow fields based on Latent Dirichlet allocation (LDA) model. Analogous to topic modeling in text analysis, in our approach, pathlines and features in a given flow field are defined as documents and words respectively. Flow topics are then extracted based on Latent Dirichlet allocation. Different from other feature extraction methods, our approach clusters pathlines with probabilistic assignment, and aggregates features to meaningful topics at the same time. We build a prototype system to support exploration of unsteady flow field with our proposed LDA-based method. Interactive techniques are also developed to explore the extracted topics and to gain insight from the data. We conduct case studies to demonstrate the effectiveness of our proposed approach.