Conditional Parallel Coordinates

Parallel Coordinates are a popular data visualization technique for multivariate data. Dating back to as early as 1880 PC are nearly as old as John Snow's famous cholera outbreak map of 1855, which is frequently regarded as a historic landmark for modern data visualization. Numerous extensions have been proposed to address integrity, scalability and readability. We make a new case to employ PC on conditional data, where additional dimensions are only unfolded if certain criteria are met in an observation. Compared to standard PC which operate on a flat set of dimensions the ontology of our input to Conditional Parallel Coordinates is of hierarchical nature. We therefore briefly review related work around hierarchical PC using aggregation or nesting techniques. Our contribution is a visualization to seamlessly adapt PC for conditional data under preservation of intuitive interaction patterns to select or highlight polylines. We conclude with intuitions on how to operate CPC on two data sets: an AutoML hyperparameter search log, and session results from a conversational agent.Comment: 5 pages, 8 figures, VIS 2019 Short Paper

On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.Comment: Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthda

Angle-Uniform Parallel Coordinates

We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.Comment: Computational Visual Media, 202

Speaking Stata: Graphing agreement and disagreement

Many statistical problems involve comparison and, in particular, the assessment of agreement or disagreement between data measured on identical scales. Some commonly used plots are often ineffective in assessing the fine structure of such data, especially scatterplots of highly correlated variables and plots of values measured "before" and "after" using tilted line segments. Valuable alternatives are available using horizontal reference patterns, changes plotted as parallel lines, and parallel coordinates plots. The quantities of interest (usually differences on some scale) should be shown as directly as possible, and the responses of given individuals should be identified as easily as possible. Copyright 2004 by StataCorp LP.graphics, comparison, agreement, paired data, panel data, scatterplot, difference-mean plot, Bland-Altman plot, parallel lines plot, parallel coordinates plot, pairplot, parplot, linkplot, Tukey