Cluster-aware arrangement of the parallel coordinate plots

Abstract The dimension ordering of parallel coordinate plots has been widely studied, aiming at the insightful exploration of multi-dimensional data. However, few works focus on the category distributions across dimensions and construct an effective dimension ordering to enable the visual exploration of clusters. Therefore, we propose a cluster-aware arrangement method of the parallel coordinate plots and design a visualization framework for the multi-dimensional data exploration. Firstly, a hierarchical clustering scheme is employed to identify the categories of interest across different dimensions. Then we design a group of icicle views to present the hierarchies of dimensions, the colors of which also indicate the relationships between different categories. A cluster-aware correlation is defined to measure the relationships between different attribute axes, based on the distributions of categories. Furthermore, a matrix map is designed to present the relationships between dimensions, and the MDS method is employed to transform the dimensions into 2D coordinates, in which the correlations among the dimensions are conserved. At last, we solve the Traveling Salesman Problem (TSP) and achieve an automated dimension ordering of the parallel coordinate plots, which largely highlights the relations of categories across dimensions. A set of convenient interactions are also integrated in the visualization system, allowing users to get insights into the multi-dimensional data from various perspectives. A large number of experimental results and the credible user studies further demonstrate the usefulness of the cluster-aware arrangement of the parallel coordinate plots.

[1]  Xiaotong Liu,et al.  Multi-Resolution Climate Ensemble Parameter Analysis with Nested Parallel Coordinates Plots , 2017, IEEE Transactions on Visualization and Computer Graphics.

[2]  Xiaoru Yuan,et al.  Dimension Projection Matrix/Tree: Interactive Subspace Visual Exploration and Analysis of High Dimensional Data , 2013, IEEE Transactions on Visualization and Computer Graphics.

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

[4]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[5]  Xin Zhao,et al.  Structure revealing techniques based on parallel coordinates plot , 2012, The Visual Computer.

[6]  Ping Guo,et al.  Visual Analysis of the Air Pollution Problem in Hong Kong , 2007, IEEE Transactions on Visualization and Computer Graphics.

[7]  Hans-Peter Kriegel,et al.  Recursive pattern: a technique for visualizing very large amounts of data , 1995, Proceedings Visualization '95.

[8]  Eser Kandogan.  Star Coordinates: A Multi-dimensional Visualization Technique with Uniform Treatment of Dimensions , 2000 .

[9]  Klaus Mueller,et al.  A network-based interface for the exploration of high-dimensional data spaces , 2012, 2012 IEEE Pacific Visualization Symposium.

[10]  Alfred Inselberg,et al.  Parallel Coordinates: Visual Multidimensional Geometry and Its Applications , 2003, KDIR.

[11]  Hans-Peter Seidel,et al.  An Edge-Bundling Layout for Interactive Parallel Coordinates , 2014, 2014 IEEE Pacific Visualization Symposium.

[12]  Jarke J. van Wijk,et al.  Eurographics/ieee-vgtc Symposium on Visualization 2010 Evaluation of Cluster Identification Performance for Different Pcp Variants , 2022 .

[13]  Diansheng Guo,et al.  Coordinating Computational and Visual Approaches for Interactive Feature Selection and Multivariate Clustering , 2003, Inf. Vis..

[14]  Matthew O. Ward,et al.  Interactive hierarchical dimension ordering, spacing and filtering for exploration of high dimensional datasets , 2003, IEEE Symposium on Information Visualization 2003 (IEEE Cat. No.03TH8714).

[15]  Daniel A. Keim,et al.  Pixel bar charts: a visualization technique for very large multi-attribute data sets? , 2002, Inf. Vis..

[16]  Herman Chernoff,et al.  The Use of Faces to Represent Points in k- Dimensional Space Graphically , 1973 .

[17]  Igor Jurisica,et al.  The FlowVizMenu and Parallel Scatterplot Matrix: Hybrid Multidimensional Visualizations for Network Exploration , 2010, IEEE Transactions on Visualization and Computer Graphics.

[18]  Klaus Mueller,et al.  A Visual Analytics Approach for Categorical Joint Distribution Reconstruction from Marginal Projections , 2017, IEEE Transactions on Visualization and Computer Graphics.

[19]  I. Jolliffe.  Principal Component Analysis , 2002 .

[20]  John M. Chambers,et al.  Graphical Methods for Data Analysis , 1983 .

[21]  Alfred Inselberg,et al.  Parallel coordinates for visualizing multi-dimensional geometry , 1987 .

[22]  Marcus A. Magnor,et al.  Quality-Based Visualization Matrices , 2009, VMV.

[23]  Martin Graham,et al.  Using curves to enhance parallel coordinate visualisations , 2003, Proceedings on Seventh International Conference on Information Visualization, 2003. IV 2003..

[24]  Matthew O. Ward,et al.  Clutter Reduction in Multi-Dimensional Data Visualization Using Dimension Reordering , 2004 .

[25]  J. Hartigan.  Printer graphics for clustering , 1975 .

[26]  W. Torgerson.  Multidimensional scaling: I. Theory and method , 1952 .

[27]  Lionel M. Ni,et al.  TelCoVis: Visual Exploration of Co-occurrence in Urban Human Mobility Based on Telco Data , 2016, IEEE Transactions on Visualization and Computer Graphics.

[28]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[29]  Liz J. Stuart,et al.  Animator: a tool for the animation of parallel coordinates , 2004 .

[30]  Daniel Weiskopf,et al.  State of the Art of Parallel Coordinates , 2013, Eurographics.