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.

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.

Multivariate measurements taken at irregularly sampled locations are a common form of data, for example in geochemical analysis of soil. In practical considerations predictions of these measurements at unobserved locations are of great interest. For standard multivariate spatial prediction methods it is mandatory to not only model spatial dependencies but also cross-dependencies which makes it a demanding task. Recently, a blind source separation approach for spatial data was suggested. When using this spatial blind source separation method prior the actual spatial prediction, modelling of spatial cross-dependencies is avoided, which in turn simplifies the spatial prediction task significantly. In this paper we investigate the use of spatial blind source separation as a pre-processing tool for spatial prediction and compare it with predictions from Cokriging and neural networks in an extensive simulation study as well as a geochemical dataset.