Continuous Parallel Coordinates

Typical scientific data is represented on a grid with appropriate interpolation or approximation schemes,defined on a continuous domain. The visualization of such data in parallel coordinates may reveal patterns latently contained in the data and thus can improve the understanding of multidimensional relations. In this paper, we adopt the concept of continuous scatterplots for the visualization of spatially continuous input data to derive a density model for parallel coordinates. Based on the point-line duality between scatterplots and parallel coordinates, we propose a mathematical model that maps density from a continuous scatterplot to parallel coordinates and present different algorithms for both numerical and analytical computation of the resulting density field. In addition, we show how the 2-D model can be used to successively construct continuous parallel coordinates with an arbitrary number of dimensions. Since continuous parallel coordinates interpolate data values within grid cells, a scalable and dense visualization is achieved, which will be demonstrated for typical multi-variate scientific data.

[1]  Edward J. Wegman,et al.  High Dimensional Clustering Using Parallel Coordinates and the Grand Tour , 1997 .

[2]  Alan J. Dix,et al.  Enabling Automatic Clutter Reduction in Parallel Coordinate Plots , 2006, IEEE Transactions on Visualization and Computer Graphics.

[3]  Helwig Hauser,et al.  Angular brushing of extended parallel coordinates , 2002, IEEE Symposium on Information Visualization, 2002. INFOVIS 2002..

[4]  E. Wegman,et al.  Construction of line densities for parallel coordinate plots , 1992 .

[5]  Cláudio T. Silva,et al.  Revisiting Histograms and Isosurface Statistics , 2008, IEEE Transactions on Visualization and Computer Graphics.

[6]  Charl P. Botha,et al.  Extensions of Parallel Coordinates for Interactive Exploration of Large Multi-Timepoint Data Sets , 2008, IEEE Transactions on Visualization and Computer Graphics.

[7]  Klaus Mueller,et al.  Eurographics/ Ieee-vgtc Symposium on Visualization 2008 Illustrative Parallel Coordinates , 2022 .

[8]  Matthew O. Ward,et al.  Hierarchical parallel coordinates for exploration of large datasets , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[9]  Helwig Hauser,et al.  Interactive Feature Specification for Focus+Context Visualization of Complex Simulation Data , 2003, VisSym.

[10]  Bernhard Preim,et al.  A Four‐level Focus+Context Approach to Interactive Visual Analysis of Temporal Features in Large Scientific Data , 2008, Comput. Graph. Forum.

[11]  Richard A. Becker,et al.  Brushing scatterplots , 1987 .

[12]  E. Wegman.  Hyperdimensional Data Analysis Using Parallel Coordinates , 1990 .

[13]  Daniel Weiskopf,et al.  Efficient and Adaptive Rendering of 2‐D Continuous Scatterplots , 2009, Comput. Graph. Forum.

[14]  Haim Levkowitz,et al.  Uncovering Clusters in Crowded Parallel Coordinates Visualizations , 2004, IEEE Symposium on Information Visualization.

[15]  Daniel Weiskopf,et al.  Continuous Scatterplots , 2008, IEEE Transactions on Visualization and Computer Graphics.

[16]  Matthew D. Cooper,et al.  Revealing Structure within Clustered Parallel Coordinates Displays , 2005, INFOVIS.

[17]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[18]  Helwig Hauser,et al.  Smooth Brushing for Focus+Context Visualization of Simulation Data in 3D , 2002, WSCG.

[19]  Alfred Inselberg,et al.  Multidimensional Lines II: Proximity and Applications , 1994, SIAM J. Appl. Math..

[20]  Hong Zhou,et al.  Visual Clustering in Parallel Coordinates , 2008, Comput. Graph. Forum.

[21]  Alfred Inselberg,et al.  Parallel coordinates: a tool for visualizing multi-dimensional geometry , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.

[22]  Alfred Inselberg,et al.  The plane with parallel coordinates , 1985, The Visual Computer.

[23]  Peter Shirley,et al.  A polygonal approximation to direct scalar volume rendering , 1990, SIGGRAPH 1990.

[24]  José Fernando Rodrigues,et al.  Frequency plot and relevance plot to enhance visual data exploration , 2003, 16th Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI 2003).

[25]  Hamish A. Carr,et al.  On Histograms and Isosurface Statistics , 2006, IEEE Transactions on Visualization and Computer Graphics.

[26]  Helwig Hauser,et al.  Outlier-Preserving Focus+Context Visualization in Parallel Coordinates , 2006, IEEE Transactions on Visualization and Computer Graphics.

[27]  Lawrence O. Hall,et al.  Visualizing fuzzy points in parallel coordinates , 2003, IEEE Trans. Fuzzy Syst..

[28]  Helwig Hauser,et al.  Parallel Sets: Visual Analysis of Categorical Data , 2005, INFOVIS.