In various scientific and industrial domains, analyzing multivariate spatial data, i.e., vectors associated with spatial locations, is common practice. To analyze those datasets, analysts may turn to methods such as Spatial Blind Source Separation (SBSS). Designed explicitly for spatial data analysis, SBSS finds latent components in the dataset and is superior to popular non-spatial methods, like PCA. However, when analysts try different tuning parameter settings, the amount of latent components complicates analytical tasks. Based on our years-long collaboration with SBSS researchers, we propose a visualization approach to tackle this challenge. The main component is UnDRground Tubes (UT), a general-purpose idiom combining ideas from set visualization and multidimensional projections. We describe the UT visualization pipeline and integrate UT into an interactive multiple-view system. We demonstrate its effectiveness through interviews with SBSS experts, a qualitative evaluation with visualization experts, and computational experiments. SBSS experts were excited about our approach. They saw many benefits for their work and potential applications for geostatistical data analysis more generally. UT was also well received by visualization experts. Our benchmarks show that UT projections and its heuristics are appropriate.

Real-world datasets often consist of quantitative and categorical variables. The analyst needs to focus on either kind separately or both jointly. We proposed a visualization technique tackling these challenges that supports visual cluster and set analysis. In this paper, we investigate how its visualization parameters affect the accuracy and speed of cluster and set analysis tasks in a controlled experiment. Our findings show that, with the proper settings, our visualization can support both task types well. However, we did not find settings suitable for the joint task, which provides opportunities for future research.

The dynamic network visualization design space consists of two major dimensions: network structural and temporal representation. As more techniques are developed and published, a clear need for evaluation and experimental comparisons between them emerges. Most studies explore the temporal dimension and diverse interaction techniques supporting the participants, focusing on a single structural representation. Empirical evidence about performance and preference for different visualization approaches is scattered over different studies, experimental settings, and tasks. This paper aims to comprehensively investigate the dynamic network visualization design space in two evaluations. First, a controlled study assessing participants' response times, accuracy, and preferences for different combinations of network structural and temporal representations on typical dynamic network exploration tasks, with and without the support of standard interaction methods. Second, the best-performing combinations from the first study are enhanced based on participants' feedback and evaluated in a heuristic-based qualitative study with visualization experts on a real-world network. Our results highlight node-link with animation and playback controls as the best-performing combination and the most preferred based on ratings. Matrices achieve similar performance to node-link in the first study but have considerably lower scores in our second evaluation. Similarly, juxtaposition exhibits evident scalability issues in more realistic analysis contexts.

Modern science and industry rely on computational models for simulation, prediction, and data analysis. Spatial blind source separation (SBSS) is a model used to analyze spatial data. Designed explicitly for spatial data analysis, it is superior to popular non-spatial methods, like PCA. However, a challenge to its practical use is setting two complex tuning parameters, which requires parameter space analysis. In this paper, we focus on sensitivity analysis (SA). SBSS parameters and outputs are spatial data, which makes SA difficult as few SA approaches in the literature assume such complex data on both sides of the model. Based on the requirements in our design study with statistics experts, we developed a visual analytics prototype for data type agnostic visual sensitivity analysis that fits SBSS and other contexts. The main advantage of our approach is that it requires only dissimilarity measures for parameter settings and outputs (Fig. 1). We evaluated the prototype heuristically with visualization experts and through interviews with two SBSS experts. In addition, we show the transferability of our approach by applying it to microclimate simulations. Study participants could confirm suspected and known parameter-output relations, find surprising associations, and identify parameter subspaces to examine in the future. During our design study and evaluation, we identified challenging future research opportunities.

Computational models, such as simulations, are central to a wide range of fields in science and industry. Those models take input parameters and produce some output. To fully exploit their utility, relations between parameters and outputs must be understood. These include, for example, which parameter setting produces the best result (optimization) or which ranges of parameter settings produce a wide variety of results (sensitivity). Such tasks are often difficult to achieve for various reasons, for example, the size of the parameter space, and supported with visual analytics. In this paper, we survey visual parameter space exploration (VPSE) systems involving spatial and temporal data. We focus on interactive visualizations and user interfaces. Through thematic analysis of the surveyed papers, we identify common workflow steps and approaches to support them. We also identify topics for future work that will help enable VPSE on a greater variety of computational models.

Analysis of spatial multivariate data, i.e., measurements at irregularly-spaced locations, is a challenging topic in visualization and statistics alike. Such data are inteGral to many domains, e.g., indicators of valuable minerals are measured for mine prospecting. Popular analysis methods, like PCA, often by design do not account for the spatial nature of the data. Thus they, together with their spatial variants, must be employed very carefully. Clearly, it is preferable to use methods that were specifically designed for such data, like spatial blind source separation (SBSS). However, SBSS requires two tuning parameters, which are themselves complex spatial objects. Setting these parameters involves navigating two large and interdependent parameter spaces, while also taking into account prior knowledge of the physical reality represented by the data. To support analysts in this process, we developed a visual analytics prototype. We evaluated it with experts in visualization, SBSS, and geochemistry. Our evaluations show that our interactive prototype allows to define complex and realistic parameter settings efficiently, which was so far impractical. Settings identified by a non-expert led to remarkable and surprising insights for a domain expert. Therefore, this paper presents important first steps to enable the use of a promising analysis method for spatial multivariate data.

Temporal Blind Source Separation (TBSS) is used to obtain the true underlying processes from noisy temporal multivariate data, such as electrocardiograms. TBSS has similarities to Principal Component Analysis (PCA) as it separates the input data into univariate components and is applicable to suitable datasets from various domains, such as medicine, finance, or civil engineering. Despite TBSS’s broad applicability, the involved tasks are not well supported in current tools, which offer only text-based interactions and single static images. Analysts are limited in analyzing and comparing obtained results, which consist of diverse data such as matrices and sets of time series. Additionally, parameter settings have a big impact on separation performance, but as a consequence of improper tooling, analysts currently do not consider the whole parameter space. We propose to solve these problems by applying visual analytics (VA) principles. Our primary contribution is a design study for TBSS, which so far has not been explored by the visualization community. We developed a task abstraction and visualization design in a user-centered design process. Task-specific assembling of well-established visualization techniques and algorithms to gain insights in the TBSS processes is our secondary contribution. We present TBSSvis, an interactive web-based VA prototype, which we evaluated extensively in two interviews with five TBSS experts. Feedback and observations from these interviews show that TBSSvis supports the actual workflow and combination of interactive visualizations that facilitate the tasks involved in analyzing TBSS results.

Preprocessing is a mandatory first step to make data usable for analysis. While in time series analysis many established methods require data that are sampled in regular time intervals, in practice sensors may sample data at varying interval lengths. Time series rastering is the process of aggregating unequally spaced time series into equal interval lengths. In this paper we discuss critical aspects in the context of time series rastering, and we present a visual design which supports the parametrization of the rastering transformation, communicates the introduced uncertainties and quality issues, and facilitates the comparison of alternative rastering outcomes to achieve optimal results.

Abstract The cycle plot is an established and effective visualization technique for identifying and comprehending patterns in periodic time series, like trends and seasonal cycles. It also allows to visually identify and contextualize extreme values and outliers from a different perspective. Unfortunately, it is limited to univariate data. For multivariate time series, patterns that exist across several dimensions are much harder or impossible to explore. We propose a modified cycle plot using a distance‐based abstraction (Mahalanobis distance) to reduce multiple dimensions to one overview dimension and retain a representation similar to the original. Utilizing this distance‐based cycle plot in an interactive exploration environment, we enhance the Visual Analytics capacity of cycle plots for multivariate outlier detection. To enable interactive exploration and interpretation of outliers, we employ coordinated multiple views that juxtapose a distance‐based cycle plot with Cleveland's original cycle plots of the underlying dimensions. With our approach it is possible to judge the outlyingness regarding the seasonal cycle in multivariate periodic time series.

A number of studies have investigated different ways of visualizing uncertainty. However, in the temporal dimension, it is still an open question how to best represent uncertainty, since the special characteristics of time require special visual encodings and may provoke different interpretations. Thus, we have conducted a comprehensive study comparing alternative visual encodings of intervals with uncertain start and end times: gradient plots, violin plots, accumulated probability plots, error bars, centered error bars, and ambiguation. Our results reveal significant differences in error rates and completion time for these different visualization types and different tasks. We recommend using ambiguation - using a lighter color value to represent uncertain regions - or error bars for judging durations and temporal bounds, and gradient plots - using fading color or transparency - for judging probability values.

Model selection in time series analysis is a challenging task for domain experts in many application areas such as epidemiology, economy, or environmental sciences. The methodology used for this task demands a close combination of human judgement and automated computation. However, statistical software tools do not adequately support this combination through interactive visual interfaces. We propose a Visual Analytics process to guide domain experts in this task. For this purpose, we developed the TiMoVA prototype that implements this process based on user stories and iterative expert feedback on user experience. The prototype was evaluated by usage scenarios with an example dataset from epidemiology and interviews with two external domain experts in statistics. The insights from the experts' feedback and the usage scenarios show that TiMoVA is able to support domain experts in model selection tasks through interactive visual interfaces with short feedback cycles.