A Visual Analytics Approach for Categorical Joint Distribution Reconstruction from Marginal Projections

Nebula: A Coordinating Grammar of Graphics

In multiple coordinated views (MCVs), visualizations across views update their content in response to users' interactions in other views. Interactive systems provide direct manipulation to create coordination between views, but are restricted to limited types of predefined templates. By contrast, textual specification languages enable flexible coordination but expose technical burden. To bridge the gap, we contribute Nebula, a grammar based on natural language for coordinating visualizations in MCVs. The grammar design is informed by a novel framework based on a systematic review of 176 coordinations from existing theories and applications, which describes coordination by demonstration, i.e., how coordination is performed by users. With the framework, Nebula specification formalizes coordination as a composition of user- and coordination-triggered interactions in origin and destination views, respectively, along with potential data transformation between the interactions. We evaluate Nebula by demonstrating its expressiveness with a gallery of diverse examples and analyzing its usability on cognitive dimensions.

ColorMapND: A Data-Driven Approach and Tool for Mapping Multivariate Data to Color

A wide variety of color schemes have been devised for mapping scalar data to color. We address the challenge of color-mapping multivariate data. While a number of methods can map low-dimensional data to color, for example, using bilinear or barycentric interpolation for two or three variables, these methods do not scale to higher data dimensions. Likewise, schemes that take a more artistic approach through color mixing and the like also face limits when it comes to the number of variables they can encode. Our approach does not have these limitations. It is data driven in that it determines a proper and consistent color map from first embedding the data samples into a circular interactive multivariate color mapping display (ICD) and then fusing this display with a convex (CIE HCL) color space. The variables (data attributes) are arranged in terms of their similarity and mapped to the ICD's boundary to control the embedding. Using this layout, the color of a multivariate data sample is then obtained via modified generalized barycentric coordinate interpolation of the map. The system we devised has facilities for contrast and feature enhancement, supports both regular and irregular grids, can deal with multi-field as well as multispectral data, and can produce heat maps, choropleth maps, and diagrams such as scatterplots.

Evaluating Multi-Dimensional Visualizations for Understanding Fuzzy Clusters

Fuzzy clustering assigns a probability of membership for a datum to a cluster, which veritably reflects real-world clustering scenarios but significantly increases the complexity of understanding fuzzy clusters. Many studies have demonstrated that visualization techniques for multi-dimensional data are beneficial to understand fuzzy clusters. However, no empirical evidence exists on the effectiveness and efficiency of these visualization techniques in solving analytical tasks featured by fuzzy clusters. In this paper, we conduct a controlled experiment to evaluate the ability of fuzzy clusters analysis to use four multi-dimensional visualization techniques, namely, parallel coordinate plot, scatterplot matrix, principal component analysis, and Radviz. First, we define the analytical tasks and their representative questions specific to fuzzy clusters analysis. Then, we design objective questionnaires to compare the accuracy, time, and satisfaction in using the four techniques to solve the questions. We also design subjective questionnaires to collect the experience of the volunteers with the four techniques in terms of ease of use, informativeness, and helpfulness. With a complete experiment process and a detailed result analysis, we test against four hypotheses that are formulated on the basis of our experience, and provide instructive guidance for analysts in selecting appropriate and efficient visualization techniques to analyze fuzzy clusters.

SIRIUS: Dual, Symmetric, Interactive Dimension Reductions

Much research has been done regarding how to visualize and interact with observations and attributes of high-dimensional data for exploratory data analysis. From the analyst's perceptual and cognitive perspective, current visualization approaches typically treat the observations of the high-dimensional dataset very differently from the attributes. Often, the attributes are treated as inputs (e.g., sliders), and observations as outputs (e.g., projection plots), thus emphasizing investigation of the observations. However, there are many cases in which analysts wish to investigate both the observations and the attributes of the dataset, suggesting a symmetry between how analysts think about attributes and observations. To address this, we define SIRIUS (Symmetric Interactive Representations In a Unified System), a symmetric, dual projection technique to support exploratory data analysis of high-dimensional data. We provide an example implementation of SIRIUS and demonstrate how this symmetry affords additional insights.