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Scatterplots are a fundamental method for visual data analysis, but they often suffer from severe overplotting. Density-equalizing transformations can mitigate this by redistributing points to a uniform density. While Optimal Transport (OT) provides a robust mathematical framework for density equalization, existing numerical solvers are often computationally expensive, complex to implement, and difficult to adapt for specific application constraints. We present a scalable, multiresolution algorithm for scatterplot regularization that approaches the high-quality structural preservation of exact OT solvers. Our method constructs a displacement field by merging local, analytically solved 2×2 patch optimizations into a globally consistent mesh, repeating this process across multiple resolutions. We systematically evaluate local solvers, interpolation schemes, and scheduling strategies to balance transport cost, distortion errors, and runtime efficiency. The approach is straightforward to implement, supports local constraints, and generalizes mathematically to higher dimensions. Our efficient GPU implementation processes millions of points at interactive frame rates, significantly outperforming existing OT solvers. Quantitative and qualitative comparisons demonstrate that our method enhances uniformity while minimizing distortion, even under extreme density variations. We further demonstrate the method’s versatility through applications in constrained regularization, scatterplot gridification, and image contrast enhancement.

Quality metrics play a crucial role in the proper use of dimensionality reduction projections for visual analysis of high-dimensional data. They quantify the degree of distortion of a projection compared to the high-dimensional data and provide a reliable indication of how confident users can be in the structures they see in the resulting layouts. However, most popular metrics focus on capturing direct relationships between points (e.g., distances or neighborhoods) while neglecting distortions in empty areas of the layout, even though these often compose visually relevant features of a 2D layout. In this paper, we introduce the Gap Index (GI), a quality metric for 2D projections that captures visual distortion by measuring spatial distortion in empty areas of a projection. It does so by decomposing the space into empty triangles, which are then compared to their high-dimensional counterparts to compute the deformation. This per-triangle deformation can be aggregated into a single scalar value or overlaid on a projection to visualize regional distortion patterns. Results show that, contrary to popular quality metrics, the GI is sensitive to small structural deformations that have high visual impact. It is also fast to compute and interpretable.

Confirmation bias can shape how prior beliefs influence both the perception of scatterplot correlations and the identification of outliers during data cleaning. We characterize this bias in two stages: perception bias, in which people interpret a scatterplot’s correlation in ways that align with their beliefs, and outlier bias, in which they selectively remove points to make the resulting data better match those beliefs. In a pre-registered crowdsourced study with 507 participants, we designed an interactive ‘Find Outliers’ task in which participants first expressed their prior beliefs about the relationship shown in a scatterplot before viewing it. Then, if they believed outliers were present, they identified and removed those outliers. Overall, 59% of participants removed data points. Among them, stronger prior beliefs predicted greater perception and outlier bias. They also tended to remove data points in ways that made the remaining data more consistent with their beliefs, especially when the outliers were less visually salient and the data were therefore more open to interpretation. Our findings show that data cleaning is not purely objective. Prior beliefs can guide how people visually identify and remove outliers. We therefore discuss how visualization systems can better support data cleaning workflows to mitigate confirmation bias.

Designing effective categorical palettes requires balancing a range of factors, including perceptual distinctiveness, category count, and task effectiveness. The effectiveness of categorical encodings can vary substantially depending on the target analytical tasks; however, existing recommendation tools largely ignore task context when evaluating palette quality, resulting in inconsistent performance across tasks. We synthesize findings from a series of multi-stage user studies into a unified model of task-based effectiveness for color encodings, shape encodings, and their redundant combination across category counts and seven common scatterplot tasks. Our results show that task and palette choice jointly influence perceptual accuracy: different color and shape palettes exhibit varying levels of robustness across tasks, indicating that palette effectiveness is task-dependent. We estimate task-specific perceptual strengths for 39 colors and 39 shapes using Bradley-Terry models, refined through adaptive sampling to target uncertain and task-sensitive comparisons. We further quantify cross-channel interactions using a redundant gain Delta G metric to model performance across color and shape pairings. We then train a predictive model that scores candidate palettes based on task, category count, and perceptual features. This model drives effective palette recommendations in CatPAL, a task-aware palette recommendation system grounded in empirical data responsive to user constraints. Our findings highlight the importance of selecting categorical palettes aligned with specific analytical tasks and demonstrate how task-aware modeling enables more reliable palette design. CatPAL translates empirical results into a practical tool that supports user-specified colors or shapes and returns ranked palette recommendations adaptable to a range of tasks.

Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots that visually capture some properties of the data. Because visually determining the accuracy of these plots is challenging, researchers often use quality metrics to measure the projection’s accuracy and faithfulness to the original data. One of the most commonly employed metrics, normalized stress, is sensitive to uniform scaling (stretching, shrinking) of the projection, despite this act not meaningfully changing anything about the projection. Another quality metric, the Kullback–Leibler (KL) divergence used in the popular t-Distributed Stochastic Neighbor Embedding (t-SNE) technique, is also susceptible to this scale sensitivity. We investigate the effect of scaling on stress and KL divergence analytically and empirically by showing just how much the values change and how this affects dimension reduction technique evaluations. We introduce a simple technique to make both metrics scale-invariant and show that it accurately captures expected behavior on a small benchmark.

Misuses of t-SNE and UMAP in visual analytics have become increasingly common. For example, although t-SNE and UMAP projections often do not faithfully reflect the original distances between clusters, practitioners frequently use them to investigate inter-cluster relationships. We investigate why this misuse occurs, and discuss methods to prevent it. To that end, we first review 136 papers to verify the prevalence of the misuse. We then interview researchers who have used dimensionality reduction (DR) to understand why such misuse occurs. Finally, we interview DR experts to examine why previous efforts failed to address the misuse. We find that the misuse of t-SNE and UMAP stems primarily from limited DR literacy among practitioners, and that existing attempts to address this issue—mostly based on academic papers—have been ineffective. Based on these insights, we discuss potential future research directions to mitigate the misuse.

Multivariate data contain an abundance of information and many techniques have been proposed to allow humans to navigate this information in an ordered fashion. For this work, we focus on methods that seek to convey multivariate data as a collection of bivariate scatterplots or parallel coordinates plots. Presenting multivariate data in this way requires a regime that determines in what order the bivariate scatterplots are presented or in what order the parallel coordinate axes are arranged. We refer to this order as a visualization sequence. Common techniques utilize standard statistical metrics like correlation, similarity or consistency. We expand on the family of statistical metrics by incorporating the rigidity of causal relationships. To capture these relationships, we first derive a causal graph from the data and then allow users to select from several semantic traversal schemes to derive the respective chart sequence. We tested the sequences with a crowd-sourced user study and a user interview to confirm that the causality-informed visualization sequences help viewers to better grasp the causal relationships that exist in the data, as opposed to sequences derived from correlations or randomization alone.