Comparative Evaluation of Animated Scatter Plot Transitions.

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.

Relaxed Dot Plots: Faithful Visualization of Samples and Their Distribution.

We introduce relaxed dot plots as an improvement of nonlinear dot plots for unit visualization. Our plots produce more faithful data representations and reduce moiré effects. Their contour is based on a customized kernel frequency estimation to match the shape of the distribution of underlying data values. Previous nonlinear layouts introduce column-centric nonlinear scaling of dot diameters for visualization of high-dynamic-range data with high peaks. We provide a mathematical approach to convert that column-centric scaling to our smooth envelope shape. This formalism allows us to use linear, root, and logarithmic scaling to find ideal dot sizes. Our method iteratively relaxes the dot layout for more correct and aesthetically pleasing results. To achieve this, we modified Lloyd's algorithm with additional constraints and heuristics. We evaluate the layouts of relaxed dot plots against a previously existing nonlinear variant and show that our algorithm produces less error regarding the underlying data while establishing the blue noise property that works against moiré effects. Further, we analyze the readability of our relaxed plots in three crowd-sourced experiments. The results indicate that our proposed technique surpasses traditional dot plots.

Nonlinear Dot Plots.

Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.