Visual analytics enables the coupling of machine learning models and humans in a tightly integrated workflow, addressing various analysis tasks. Each task poses distinct demands to analysts and decision-makers. In this survey, we focus on one canonical technique for rule-based classification, namely decision tree classifiers. We provide an overview of available visualizations for decision trees with a focus on how visualizations differ with respect to 16 tasks. Further, we investigate the types of visual designs employed, and the quality measures presented. We find that (i) interactive visual analytics systems for classifier development offer a variety of visual designs, (ii) utilization tasks are sparsely covered, (iii) beyond classifier development, node-link diagrams are omnipresent, (iv) even systems designed for machine learning experts rarely feature visual representations of quality measures other than accuracy. In conclusion, we see a potential for integrating algorithmic techniques, mathematical quality measures, and tailored interactive visualizations to enable human experts to utilize their knowledge more effectively.

Many processes, from gene interaction in biology to computer networks to social media, can be modeled more precisely as temporal hypergraphs than by regular graphs. This is because hypergraphs generalize graphs by extending edges to connect any number of vertices, allowing complex relationships to be described more accurately and predict their behavior over time. However, the interactive exploration and seamless refinement of such hypergraph-based prediction models still pose a major challenge. We contribute Hyper-Matrix, a novel visual analytics technique that addresses this challenge through a tight coupling between machine-learning and interactive visualizations. In particular, the technique incorporates a geometric deep learning model as a blueprint for problem-specific models while integrating visualizations for graph-based and category-based data with a novel combination of interactions for an effective user-driven exploration of hypergraph models. To eliminate demanding context switches and ensure scalability, our matrix-based visualization provides drill-down capabilities across multiple levels of semantic zoom, from an overview of model predictions down to the content. We facilitate a focused analysis of relevant connections and groups based on interactive user-steering for filtering and search tasks, a dynamically modifiable partition hierarchy, various matrix reordering techniques, and interactive model feedback. We evaluate our technique in a case study and through formative evaluation with law enforcement experts using real-world internet forum communication data. The results show that our approach surpasses existing solutions in terms of scalability and applicability, enables the incorporation of domain knowledge, and allows for fast search-space traversal. With the proposed technique, we pave the way for the visual analytics of temporal hypergraphs in a wide variety of domains.

Visualization has been deemed a useful technique by researchers and practitioners, alike, leaving a trail of arguments behind that reason why visualization works. In addition, examples of misleading usages of visualizations in information communication have occasionally been pointed out. Thus, to contribute to the fundamental understanding of our discipline, we require a comprehensive collection of arguments on "why visualize?" (or "why not?"), untangling the rationale behind positive and negative viewpoints. In this paper, we report a theoretical study to understand the underlying reasons of various arguments; their relationships (e.g., built-on, and conflict); and their respective dependencies on tasks, users, and data. We curated an argumentative network based on a collection of arguments from various fields, including information visualization, cognitive science, psychology, statistics, philosophy, and others. Our work proposes several categorizations for the arguments, and makes their relations explicit. We contribute the first comprehensive and systematic theoretical study of the arguments on visualization. Thereby, we provide a roadmap towards building a foundation for visualization theory and empirical research as well as for practical application in the critique and design of visualizations. In addition, we provide our argumentation network and argument collection online at https://whyvis.dbvis.de, supported by an interactive visualization.

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach.

Five years after the first state-of-the-art report on Commercial Visual Analytics Systems we present a reevaluation of the Big Data Analytics field. We build on the success of the 2012 survey, which was influential even beyond the boundaries of the InfoVis and Visual Analytics (VA) community. While the field has matured significantly since the original survey, we find that innovation and research-driven development are increasingly sacrificed to satisfy a wide range of user groups. We evaluate new product versions on established evaluation criteria, such as available features, performance, and usability, to extend on and assure comparability with the previous survey. We also investigate previously unavailable products to paint a more complete picture of the commercial VA landscape. Furthermore, we introduce novel measures, like suitability for specific user groups and the ability to handle complex data types, and undertake a new case study to highlight innovative features. We explore the achievements in the commercial sector in addressing VA challenges and propose novel developments that should be on systems' roadmaps in the coming years.