Winglets: Visualizing Association with Uncertainty in Multi-class Scatterplots

A Framework for Multiclass Contour Visualization

Multiclass contour visualization is often used to interpret complex data attributes in such fields as weather forecasting, computational fluid dynamics, and artificial intelligence. However, effective and accurate representations of underlying data patterns and correlations can be challenging in multiclass contour visualization, primarily due to the inevitable visual cluttering and occlusions when the number of classes is significant. To address this issue, visualization design must carefully choose design parameters to make visualization more comprehensible. With this goal in mind, we proposed a framework for multiclass contour visualization. The framework has two components: a set of four visualization design parameters, which are developed based on an extensive review of literature on contour visualization, and a declarative domain-specific language (DSL) for creating multiclass contour rendering, which enables a fast exploration of those design parameters. A task-oriented user study was conducted to assess how those design parameters affect users' interpretations of real-world data. The study results offered some suggestions on the value choices of design parameters in multiclass contour visualization.

Implicit Multidimensional Projection of Local Subspaces

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.

Temporal scatterplots

Visualizing high-dimensional data on a 2D canvas is generally challenging. It becomes significantly more difficult when multiple time-steps are to be presented, as the visual clutter quickly increases. Moreover, the challenge to perceive the significant temporal evolution is even greater. In this paper, we present a method to plot temporal high-dimensional data in a static scatterplot; it uses the established PCA technique to project data from multiple time-steps. The key idea is to extend each individual displacement prior to applying PCA, so as to skew the projection process, and to set a projection plane that balances the directions of temporal change and spatial variance. We present numerous examples and various visual cues to highlight the data trajectories, and demonstrate the effectiveness of the method for visualizing temporal data.