Matching visual saliency to confidence in plots of uncertain data

De-Cluttering Scatterplots With Integral Images

Scatterplots provide a visual representation of bivariate data (or 2D embeddings of multivariate data) that allows for effective analyses of data dependencies, clusters, trends, and outliers. Unfortunately, classical scatterplots suffer from scalability issues, since growing data sizes eventually lead to overplotting and visual clutter on a screen with a fixed resolution, which hinders the data analysis process. We propose an algorithm that compensates for irregular sample distributions by a smooth transformation of the scatterplot's visual domain. Our algorithm evaluates the scatterplot's density distribution to compute a regularization mapping based on integral images of the rasterized density function. The mapping preserves the samples' neighborhood relations. Few regularization iterations suffice to achieve a nearly uniform sample distribution that efficiently uses the available screen space. We further propose approaches to visually convey the transformation that was applied to the scatterplot and compare them in a user study. We present a novel parallel algorithm for fast GPU-based integral-image computation, which allows for integrating our de-cluttering approach into interactive visual data analysis systems.

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.

KD-Box: Line-segment-based KD-tree for Interactive Exploration of Large-scale Time-Series Data

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.

The Science of Visual Data Communication: What Works

Effectively designed data visualizations allow viewers to use their powerful visual systems to understand patterns in data across science, education, health, and public policy. But ineffectively designed visualizations can cause confusion, misunderstanding, or even distrust-especially among viewers with low graphical literacy. We review research-backed guidelines for creating effective and intuitive visualizations oriented toward communicating data to students, coworkers, and the general public. We describe how the visual system can quickly extract broad statistics from a display, whereas poorly designed displays can lead to misperceptions and illusions. Extracting global statistics is fast, but comparing between subsets of values is slow. Effective graphics avoid taxing working memory, guide attention, and respect familiar conventions. Data visualizations can play a critical role in teaching and communication, provided that designers tailor those visualizations to their audience.

Uncertainty in Continuous Scatterplots, Continuous Parallel Coordinates, and Fibers

In this paper, we introduce uncertainty to continuous scatterplots and continuous parallel coordinates. We derive respective models, validate them with sampling-based brute-force schemes, and present acceleration strategies for their computation. At the same time, we show that our approach lends itself as well for introducing uncertainty into the definition of fibers in bivariate data. Finally, we demonstrate the properties and the utility of our approach using specifically designed synthetic cases and simulated data.

Bayesian-Assisted Inference from Visualized Data

A Bayesian view of data interpretation suggests that a visualization user should update their existing beliefs about a parameter's value in accordance with the amount of information about the parameter value captured by the new observations. Extending recent work applying Bayesian models to understand and evaluate belief updating from visualizations, we show how the predictions of Bayesian inference can be used to guide more rational belief updating. We design a Bayesian inference-assisted uncertainty analogy that numerically relates uncertainty in observed data to the user's subjective uncertainty, and a posterior visualization that prescribes how a user should update their beliefs given their prior beliefs and the observed data. In a pre-registered experiment on 4,800 people, we find that when a newly observed data sample is relatively small (N=158), both techniques reliably improve people's Bayesian updating on average compared to the current best practice of visualizing uncertainty in the observed data. For large data samples (N=5208), where people's updated beliefs tend to deviate more strongly from the prescriptions of a Bayesian model, we find evidence that the effectiveness of the two forms of Bayesian assistance may depend on people's proclivity toward trusting the source of the data. We discuss how our results provide insight into individual processes of belief updating and subjective uncertainty, and how understanding these aspects of interpretation paves the way for more sophisticated interactive visualizations for analysis and communication.

Visual Analysis of Large Multivariate Scattered Data using Clustering and Probabilistic Summaries

Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large scattered datasets. In contrast to previous approaches that represent blocks of volumetric data using probability distributions, we model clusters of arbitrarily structured multivariate data. In detail, we discuss how to efficiently represent and store a high-dimensional distribution for each cluster. We observe that it suffices to consider low-dimensional marginal distributions for two or three data dimensions at a time to employ common visual analysis techniques. Based on this observation, we represent high-dimensional distributions by combinations of low-dimensional Gaussian mixture models. We discuss the application of common interactive visual analysis techniques to this representation. In particular, we investigate several frequency-based views, such as density plots in 1D and 2D, density-based parallel coordinates, and a time histogram. We visualize the uncertainty introduced by the representation, discuss a level-of-detail mechanism, and explicitly visualize outliers. Furthermore, we propose a spatial visualization by splatting anisotropic 3D Gaussians for which we derive a closed-form solution. Lastly, we describe the application of brushing and linking to this clustered representation. Our evaluation on several large, real-world datasets demonstrates the scaling of our approach.

A Recursive Subdivision Technique for Sampling Multi-class Scatterplots

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.

Data Sampling in Multi-view and Multi-class Scatterplots via Set Cover Optimization

We present a method for data sampling in scatterplots by jointly optimizing point selection for different views or classes. Our method uses space-filling curves (Z-order curves) that partition a point set into subsets that, when covered each by one sample, provide a sampling or coreset with good approximation guarantees in relation to the original point set. For scatterplot matrices with multiple views, different views provide different space-filling curves, leading to different partitions of the given point set. For multi-class scatterplots, the focus on either per-class distribution or global distribution provides two different partitions of the given point set that need to be considered in the selection of the coreset. For both cases, we convert the coreset selection problem into an Exact Cover Problem (ECP), and demonstrate with quantitative and qualitative evaluations that an approximate solution that solves the ECP efficiently is able to provide high-quality samplings.

Smart Brushing for Parallel Coordinates

The Parallel Coordinates plot is a popular tool for the visualization of high-dimensional data. One of the main challenges when using parallel coordinates is occlusion and overplotting resulting from large data sets. Brushing is a popular approach to address these challenges. Since its conception, limited improvements have been made to brushing both in the form of visual design and functional interaction. We present a set of novel, smart brushing techniques that enhance the standard interactive brushing of a parallel coordinates plot. We introduce two new interaction concepts: Higher-order, sketch-based brushing, and smart, data-driven brushing. Higher-order brushes support interactive, flexible, n-dimensional pattern searches involving an arbitrary number of dimensions. Smart, data-driven brushing provides interactive, real-time guidance to the user during the brushing process based on derived meta-data. In addition, we implement a selection of novel enhancements and user options that complement the two techniques as well as enhance the exploration and analytical ability of the user. We demonstrate the utility and evaluate the results using a case study with a large, high-dimensional, real-world telecommunication data set and we report domain expert feedback from the data suppliers.

Line Graph or Scatter Plot? Automatic Selection of Methods for Visualizing Trends in Time Series

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.

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.

Probabilistic Graph Layout for Uncertain Network Visualization

We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

Typology of Uncertainty in Static Geolocated Graphs for Visualization

Static geolocated graphs have nodes connected by edges, where both can have geographic location and associated attributes. For example, it can be uncertain exactly where a node is located or whether an edge between two nodes exists. Because source data is often incomplete or inexact, it is necessary to visualize this uncertainty to help users make appropriate decisions. The proposed typology of uncertainty extends related typologies with specific features needed for characterizing uncertainty in static geolocated graphs.

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.

Visualization for Understanding Uncertainty in Activation Volumes for Deep Brain Stimulation

We have created the Neurostimulation Uncertainty Viewer (nuView or νView) tool for exploring data arising from deep brain stimulation (DBS). Simulated volume of tissue activated (VTA), using clinical electrode placements, are recorded along with patient outcomes in the Unified Parkinson's disease rating scale (UPDRS). The data is volumetric and sparse, with multi-value patient results for each activated voxel in the simulation. νView provides a collection of visual methods to explore the activated tissue to enhance understanding of electrode usage for improved therapy with DBS.

Visual Abstraction and Exploration of Multi-class Scatterplots

Scatterplots are widely used to visualize scatter dataset for exploring outliers, clusters, local trends, and correlations. Depicting multi-class scattered points within a single scatterplot view, however, may suffer from heavy overdraw, making it inefficient for data analysis. This paper presents a new visual abstraction scheme that employs a hierarchical multi-class sampling technique to show a feature-preserving simplification. To enhance the density contrast, the colors of multiple classes are optimized by taking the multi-class point distributions into account. We design a visual exploration system that supports visual inspection and quantitative analysis from different perspectives. We have applied our system to several challenging datasets, and the results demonstrate the efficiency of our approach.

Random per-element luminance modulation for improved visual tracking

Using random per-element luminance modulation can increase the visual salience of details in a range of visualizations (2D, 3D, and ND scalar, vector, and tensor fields). Although random luminance has been used in specific designs, its wide applicability isn't reflected in visualizations, perhaps because it hasn't yet been presented as a cross-cutting technique. Adding random-luminance contrast can benefit both static and animated visualizations. The article presents perceptual reasons for this technique's effectiveness. This article has two accompanying videos, at http://youtu.be/TTaSFMvBgvg and http://youtu.be/Rx1oPMTpPA4, showing animations of cones moving through a weather simulation, with and without random luminance modulation.

The generalized sensitivity scatterplot

Scatterplots remain a powerful tool to visualize multidimensional data. However, accurately understanding the shape of multidimensional points from 2D projections remains challenging due to overlap. Consequently, there are a lot of variations on the scatterplot as a visual metaphor for this limitation. An important aspect often overlooked in scatterplots is the issue of sensitivity or local trend, which may help in identifying the type of relationship between two variables. However, it is not well known how or what factors influence the perception of trends from 2D scatterplots. To shed light on this aspect, we conducted an experiment where we asked people to directly draw the perceived trends on a 2D scatterplot. We found that augmenting scatterplots with local sensitivity helps to fill the gaps in visual perception while retaining the simplicity and readability of a 2D scatterplot. We call this augmentation the generalized sensitivity scatterplot (GSS). In a GSS, sensitivity coefficients are visually depicted as flow lines, which give a sense of continuity and orientation of the data that provide cues about the way data points are scattered in a higher dimensional space. We introduce a series of glyphs and operations that facilitate the analysis of multidimensional data sets using GSS, and validate with a number of well-known data sets for both regression and classification tasks.

Visualizing Flow of Uncertainty through Analytical Processes

Uncertainty can arise in any stage of a visual analytics process, especially in data-intensive applications with a sequence of data transformations. Additionally, throughout the process of multidimensional, multivariate data analysis, uncertainty due to data transformation and integration may split, merge, increase, or decrease. This dynamic characteristic along with other features of uncertainty pose a great challenge to effective uncertainty-aware visualization. This paper presents a new framework for modeling uncertainty and characterizing the evolution of the uncertainty information through analytical processes. Based on the framework, we have designed a visual metaphor called uncertainty flow to visually and intuitively summarize how uncertainty information propagates over the whole analysis pipeline. Our system allows analysts to interact with and analyze the uncertainty information at different levels of detail. Three experiments were conducted to demonstrate the effectiveness and intuitiveness of our design.

Increasing the perceptual salience of relationships in parallel coordinate plots

We present three extensions to parallel coordinates that increase the perceptual salience of relationships between axes in multivariate data sets: (1) luminance modulation maintains the ability to preattentively detect patterns in the presence of overplotting, (2) adding a one-vs.-all variable display highlights relationships between one variable and all others, and (3) adding a scatter plot within the parallel-coordinates display preattentively highlights clusters and spatial layouts without strongly interfering with the parallel-coordinates display. These techniques can be combined with one another and with existing extensions to parallel coordinates, and two of them generalize beyond cases with known-important axes. We applied these techniques to two real-world data sets (relativistic heavy-ion collision hydrodynamics and weather observations with statistical principal component analysis) as well as the popular car data set. We present relationships discovered in the data sets using these methods.

A visual analytics approach for models of heterogeneous cell populations

In recent years, cell population models have become increasingly common. In contrast to classic single cell models, population models allow for the study of cell-to-cell variability, a crucial phenomenon in most populations of primary cells, cancer cells, and stem cells. Unfortunately, tools for in-depth analysis of population models are still missing. This problem originates from the complexity of population models. Particularly important are methods to determine the source of heterogeneity (e.g., genetics or epigenetic differences) and to select potential (bio-)markers. We propose an analysis based on visual analytics to tackle this problem. Our approach combines parallel-coordinates plots, used for a visual assessment of the high-dimensional dependencies, and nonlinear support vector machines, for the quantification of effects. The method can be employed to study qualitative and quantitative differences among cells. To illustrate the different components, we perform a case study using the proapoptotic signal transduction pathway involved in cellular apoptosis.

From Quantification to Visualization: A Taxonomy of Uncertainty Visualization Approaches

Quantifying uncertainty is an increasingly important topic across many domains. The uncertainties present in data come with many diverse representations having originated from a wide variety of disciplines. Communicating these uncertainties is a task often left to visualization without clear connection between the quantification and visualization. In this paper, we first identify frequently occurring types of uncertainty. Second, we connect those uncertainty representations to ones commonly used in visualization. We then look at various approaches to visualizing this uncertainty by partitioning the work based on the dimensionality of the data and the dimensionality of the uncertainty. We also discuss noteworthy exceptions to our taxonomy along with future research directions for the uncertainty visualization community.

Parallel edge splatting for scalable dynamic graph visualization

We present a novel dynamic graph visualization technique based on node-link diagrams. The graphs are drawn side-byside from left to right as a sequence of narrow stripes that are placed perpendicular to the horizontal time line. The hierarchically organized vertices of the graphs are arranged on vertical, parallel lines that bound the stripes; directed edges connect these vertices from left to right. To address massive overplotting of edges in huge graphs, we employ a splatting approach that transforms the edges to a pixel-based scalar field. This field represents the edge densities in a scalable way and is depicted by non-linear color mapping. The visualization method is complemented by interaction techniques that support data exploration by aggregation, filtering, brushing, and selective data zooming. Furthermore, we formalize graph patterns so that they can be interactively highlighted on demand. A case study on software releases explores the evolution of call graphs extracted from the JUnit open source software project. In a second application, we demonstrate the scalability of our approach by applying it to a bibliography dataset containing more than 1.5 million paper titles from 60 years of research history producing a vast amount of relations between title words.