Angular-based Edge Bundled Parallel Coordinates Plot for the Visual Analysis of Large Ensemble Simulation Data

With the continuous increase in the computational power and resources of modern high-performance computing (HPC) systems, large-scale ensemble simulations have become widely used in various fields of science and engineering, and especially in meteorological and climate science. It is widely known that the simulation outputs are large time-varying, multivariate, and multivalued datasets which pose a particular challenge to the visualization and analysis tasks. In this work, we focused on the widely used Parallel Coordinates Plot (PCP) to analyze the interrelations between different parameters, such as variables, among the members. However, PCP may suffer from visual cluttering and drawing performance with the increase on the data size to be analyzed, that is, the number of polylines. To overcome this problem, we present an extension to the PCP by adding B\'{e}zier curves connecting the angular distribution plots representing the mean and variance of the inclination of the line segments between parallel axes. The proposed Angular-based Parallel Coordinates Plot (APCP) is capable of presenting a simplified overview of the entire ensemble data set while maintaining the correlation information between the adjacent variables. To verify its effectiveness, we developed a visual analytics prototype system and evaluated by using a meteorological ensemble simulation output from the supercomputer Fugaku

Double-Arc Parallel Coordinates and its Axes re-Ordering Methods

The Parallel Coordinates Plot (PCP) is a popular technique for the exploration of high-dimensional data. In many cases, researchers apply it as an effective method to analyze and mine data. However, when today's data volume is getting larger, visual clutter and data clarity become two of the main challenges in parallel coordinates plot. Although Arc Coordinates Plot (ACP) is a popular approach to address these challenges, few optimization and improvement have been made on it. In this paper, we do three main contributions on the state-of-the-art PCP methods. One approach is the improvement of visual method itself. The other two approaches are mainly on the improvement of perceptual scalability when the scale or the dimensions of the data turn to be large in some mobile and wireless practical applications. 1) We present an improved visualization method based on ACP, termed as double arc coordinates plot (DACP). It not only reduces the visual clutter in ACP, but use a dimension-based bundling method with further optimization to deals with the issues of the conventional parallel coordinates plot (PCP). 2）To reduce the clutter caused by the order of the axes and reveal patterns that hidden in the data sets，we propose our first dimensional reordering method，a contribution-based method in DACP, which is based on the singular value decomposition (SVD) algorithm. The approach computes the importance score of attributes (dimensions) of the data using SVD and visualize the dimensions from left to right in DACP according the score in SVD. 3) Moreover, a similarity-based method, which is based on the combination of nonlinear correlation coefficient and SVD algorithm, is proposed as well in the paper. To measure the correlation between two dimensions and explains how the two dimensions interact with each other，we propose a reordering method based on non-linear correlation information measurements. We mainly use mutual information to calculate the partial similarity of dimensions in high-dimensional data visualization, and SVD is used to measure global data. Lastly, we use five case scenarios to evaluate the effectiveness of DACP, and the results show that our approaches not only do well in visualizing multivariate dataset, but also effectively alleviate the visual clutter in the conventional PCP, which bring users a better visual experience

Helical close packings of ideal ropes

Closely packed conformations of helices formed on the ideal rope are considered. The pitch versus radius relations which define a closely packed helix are determined. The relations stem from the turn-to-turn distance and curvature limiting conditions. Plots of the relations are shown to cross each other. The physical sense of the crossing point is discussed.Comment: 14 pages, 10 figure

Blending aggregation and selection: Adapting parallel coordinates for the visualization of large datasets

Many of the traditional data visualization techniques, which proved to be supportive for exploratory analysis of datasets of moderate sizes, fail to fulfil their function when applied to large datasets. There are two approaches to coping with large amounts of data: data selection, when only a portion of data is displayed, and data aggregation, i.e. grouping data items and considering the groups instead of the original data. None of these approaches alone suits the needs of exploratory data analysis, which requires consideration of data on all levels: overall (considering a dataset as a whole), intermediate (viewing and comparing collective characteristics of arbitrary data subsets, or classes), and elementary (accessing individual data items). Therefore, it is necessary to combine these approaches, i.e. build a tool showing the whole set and arbitrarily defined subsets (object classes) in an aggregated way and superimposing this with a representation of arbitrarily selected individual data items. We have achieved such a combination of approaches by modifying the technique of parallel coordinate plot. These modifications are described and analysed in the paper