Neural networks are used to create parametric and invertible multidimensional data projections. In this context, parametric projections enable the embedding of previously unseen data points without requiring a complete recomputation of the projection, while invertible projections allow for the reconstruction or generation of data in the original space. In this paper, we investigate the use of autoencoder (AE) architectures for simultaneously learning parametric and inverse mappings independent of the underlying dimensionality reduction method. We introduce and compare three regularization methods for autoencoder architectures designed to learn a forward mapping into two-dimensional space induced by the projection as well as inverse mappings back into the original feature space. To evaluate their performance, we conduct a systematic study on six datasets of varying dimensionality and structural complexity, using the established projection techniques t-SNE and UMAP as training targets. Our evaluation combines both quantitative metrics and qualitative assessments. The results demonstrate that AEs, particularly when trained with Kullback–Leibler divergence regularization, can achieve high-quality reconstructions while providing users with control over the degree of smoothing in the projection. Compared to disjoint neural networks, AE architectures yield superior generative capabilities for out-of-distribution samples, while still providing comparable reconstruction quality and parametric projection accuracy. This highlights their potential for interactive data generation in use cases such as classifier evaluation and counterfactual creation.

Inverse projections enable a variety of tasks such as the exploration of classifier decision boundaries, creating counterfactual explanations, and generating synthetic data. Yet, many existing inverse projection methods are difficult to implement, challenging to predict, and sensitive to parameter settings. To address these, we propose to invert distance-preserving projections like Multidimensional Scaling (MDS) projections by using multilateration – a method used for geopositioning. Our approach finds data values for locations where no data point is projected under the key assumption that a given projection technique preserves pairwise distances among data samples in the low-dimensional space. Being based on a geometrical relationship, our technique is more interpretable than comparable machine learning-based approaches and can invert 2-dimensional projections up to D − 1 dimensional spaces if given at least D data points. We compare several strategies for multilateration point selection, show the application of our technique on three additional projection techniques apart from MDS, and use established quality metrics to evaluate its accuracy in comparison to existing inverse projections. We also show its application to computing decision maps for exploring the behavior of trained classification models. When the projection to invert captures data distances well, our inverse performs similarly to existing approaches while being interpretable and considerably simpler to compute.

Abstract One‐dimensional orderings of spatial entities have been researched in many contexts, e.g. spatial indexing structures or visualizations for spatiotemporal trend analysis. While plenty of studies have been conducted to evaluate orderings of point‐based data, polygonal shapes, despite their different topological properties, have received less attention. Existing measures to quantify errors in projections or orderings suffer from generic neighborhood definitions and over‐simplification of distances when applied to polygonal data. In this work, we address these shortcomings by introducing measures that adapt to a varying neighborhood size depending on the number of contiguous neighbors and thus, address the limitations of existing measures for polygonal shapes. To guide experts in determining a suitable ordering, we propose a user‐steerable visual analytics prototype capable of locally and globally inspecting ordering errors, investigating the impact of geographic obstacles, and comparing ordering strategies using our measures. We demonstrate the effectiveness of our approach through a use case and conducted an expert study with 8 data scientists as a qualitative evaluation of our approach. Our results show that users are capable of identifying ordering errors, comparing ordering strategies on a global and local scale, as well as assessing the impact of semantically relevant geographic obstacles.

In the early days of perceptual image quality research more than 30 years ago, the multidimensionality of distortions in perceptual space was considered important. However, research focused on scalar quality as measured by mean opinion scores. With our work, we intend to revive interest in this relevant area by presenting a first pilot dataset of annotated triplet comparisons for image quality assessment. It contains one source stimulus together with distorted versions derived from 7 distortion types at 12 levels each. Our crowdsourced and curated dataset contains roughly 50,000 responses to 7,000 triplet comparisons. We show that the multidimensional embedding of the dataset poses a challenge for many established triplet embedding algorithms. Finally, we propose a new reconstruction algorithm, dubbed logistic triplet embedding (LTE) with Tikhonov regularization. It shows promising performance. This study helps researchers to create larger datasets and better embedding techniques for multidimensional image quality. The dataset includes images and ratings and can be accessed at https://github.com/jenadeleh/multidimensionalIQA-dataset/tree/main.

Abstract The visual analysis of multivariate network data is a common yet difficult task in many domains. The major challenge is to visualize the network's topology and additional attributes for entities and their connections. Although node‐link diagrams and adjacency matrices are widespread, they have inherent limitations. Node‐link diagrams struggle to scale effectively, while adjacency matrices can fail to represent network topologies clearly. In this paper, we delve into the design space of BioFabric, which aligns entities along rows and relationships along columns, providing a way to encapsulate multiple attributes for both. We explore how we can leverage the unique opportunities offered by BioFabric's design space to visualize multivariate network data — focusing on three main categories: juxtaposed visualizations, embedded on‐node and on‐edge encoding, and transformed node and edge encoding. We complement our exploration with a quantitative assessment comparing BioFabric to adjacency matrices. We postulate that the expansive design possibilities introduced in BioFabric network visualization have the potential for the visualization of multivariate data, and we advocate for further evaluation of the associated design space. Our supplemental material is available on osf.io.

With the surge of data-driven analysis techniques, there is a rising demand for enhancing the exploration of large high-dimensional data by enabling interactions for the joint analysis of features (i.e., dimensions). Such a dual analysis of the feature space and data space is characterized by three components, 1) a view visualizing feature summaries, 2) a view that visualizes the data records, and 3) a bidirectional linking of both plots triggered by human interaction in one of both visualizations, e.g., Linking & Brushing. Dual analysis approaches span many domains, e.g., medicine, crime analysis, and biology. The proposed solutions encapsulate various techniques, such as feature selection or statistical analysis. However, each approach establishes a new definition of dual analysis. To address this gap, we systematically reviewed published dual analysis methods to investigate and formalize the key elements, such as the techniques used to visualize the feature space and data space, as well as the interaction between both spaces. From the information elicited during our review, we propose a unified theoretical framework for dual analysis, encompassing all existing approaches extending the field. We apply our proposed formalization describing the interactions between each component and relate them to the addressed tasks. Additionally, we categorize the existing approaches using our framework and derive future research directions to advance dual analysis by including state-of-the-art visual analysis techniques to improve data exploration.

Scatter plots are popular for displaying 2D data, but in practice, many data sets have more than two dimensions. For the analysis of such multivariate data, it is often necessary to switch between scatter plots of different dimension pairs, e.g., in a scatter plot matrix (SPLOM). Alternative approaches include a "grand tour" for an overview of the entire data set or creating artificial axes from dimensionality reduction (DR). A cross-cutting concern in all techniques is the ability of viewers to find correspondence between data points in different views. Previous work proposed animations to preserve the mental map between view changes and to trace points as well as clusters between scatter plots of the same underlying data set. In this article, we evaluate a variety of spline- and rotation-based view transitions in a crowdsourced user study focusing on ecological validity. Using the study results, we assess each animation's suitability for tracing points and clusters across view changes. We evaluate whether the order of horizontal and vertical rotation is relevant for task accuracy. The results show that rotations with an orthographic camera or staged expansion of a depth axis significantly outperform all other animation techniques for the traceability of individual points. Further, we provide a ranking of the animated transition techniques for traceability of individual points. However, we could not find any significant differences for the traceability of clusters. Furthermore, we identified differences by animation direction that could guide further studies to determine potential confounds for these differences. We publish the study data for reuse and provide the animation framework as a D3.js plug-in.

The visual exploration of trajectory data is crucial in domains such as animal behavior, molecular dynamics, and transportation. With the emergence of immersive technology, trajectory data, which is often inherently three-dimensional, can be analyzed in stereoscopic 3D, providing new opportunities for perception, engagement, and understanding. However, the interaction with the presented data remains a key challenge. While most applications depend on hand tracking, we see eye tracking as a promising yet under-explored interaction modality, while challenges such as imprecision or inadvertently triggered actions need to be addressed. In this work, we explore the potential of eye gaze interaction for the visual exploration of trajectory data within an AR environment. We integrate hand- and eye-based interaction techniques specifically designed for three common use cases and address known eye tracking challenges. We refine our techniques and setup based on a pilot user study (n=6) and find in a follow-up study (n=20) that gaze interaction can compete with hand-tracked interaction regarding effectiveness, efficiency, and task load for selection and cluster exploration tasks. However, time step analysis comes with higher answer times and task load. In general, we find the results and preferences to be user-dependent. Our work contributes to the field of immersive data exploration, underscoring the need for continued research on eye tracking interaction.

The prevalent usage of open-source software (OSS) has led to an increased interest in resolving potential third-party security risks by fixing common vulnerabilities and exposures (CVEs). However, even with automated code analysis tools in place, security analysts often lack the means to obtain an overview of vulnerable OSS reuse in large software organizations. In this design study, we propose VULNEX (Vulnerability Explorer), a tool to audit entire software development organizations. We introduce three complementary table based representations to identify and assess vulnerability exposures due to OSS, which we designed in collaboration with security analysts. The presented tool allows examining problematic projects and applications (repositories), third-party libraries, and vulnerabilities across a software organization. We show the applicability of our tool through a use case and preliminary expert feedback.

Abstract While there are many visualization techniques for exploring numeric data, only a few work with categorical data. One prominent example is Parallel Sets, showing data frequencies instead of data points ‐ analogous to parallel coordinates for numerical data. As nominal data does not have an intrinsic order, the design of Parallel Sets is sensitive to visual clutter due to overlaps, crossings, and subdivision of ribbons hindering readability and pattern detection. In this paper, we propose a set of quality metrics, called ParSetgnostics (Parallel Sets diagnostics), which aim to improve Parallel Sets by reducing clutter. These quality metrics quantify important properties of Parallel Sets such as overlap, orthogonality, ribbon width variance, and mutual information to optimize the category and dimension ordering. By conducting a systematic correlation analysis between the individual metrics, we ensure their distinctiveness. Further, we evaluate the clutter reduction effect of ParSetgnostics by reconstructing six datasets from previous publications using Parallel Sets measuring and comparing their respective properties. Our results show that ParSetgostics facilitates multi‐dimensional analysis of categorical data by automatically providing optimized Parallel Set designs with a clutter reduction of up to 81% compared to the originally proposed Parallel Sets visualizations.