Interactive bivariate mode trees for visual structure analysis

The number of modes in a kernel density estimation of a certain data distribution is strongly dependent on the chosen scale parameter. In this paper, we present an interactive mode tree visualization that allows to visually analyze the modality structure of a data distribution. Due to the branched structure of the bivariate mode tree, composed of many curved arcs in 3D, we need to utilize advanced techniques, including clutter removal through transparency, on demand outlier suppression or preservation, and best views, to improve the legibility of the visualization mapping.

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

[2]  David J. Marchette,et al.  The Bumpy Road to the Mode Forest , 1998 .

[3]  Henrik Wann Jensen,et al.  Global Illumination using Photon Maps , 1996, Rendering Techniques.

[4]  Helwig Hauser,et al.  Quantitative data visualization with interactive KDE surfaces , 2010, SCCG.

[5]  Yee Leung,et al.  Clustering by Scale-Space Filtering , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Stephan R. Sain,et al.  Multi-dimensional Density Estimation , 2004 .

[7]  E. Parzen On Estimation of a Probability Density Function and Mode , 1962 .

[8]  Guy Lebanon,et al.  Visualizing Incomplete and Partially Ranked Data , 2008, IEEE Transactions on Visualization and Computer Graphics.

[9]  D. W. Scott,et al.  The Mode Tree: A Tool for Visualization of Nonparametric Density Features , 1993 .

[10]  Mateu Sbert,et al.  Fast Adaptive Selection of Best Views , 2003, ICCSA.

[11]  E. Wegman,et al.  The Filtered Mode Tree , 1997 .

[12]  B. Silverman,et al.  Using Kernel Density Estimates to Investigate Multimodality , 1981 .

[13]  Yizong Cheng,et al.  Mean Shift, Mode Seeking, and Clustering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  M. Rosenblatt Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[16]  David S. Ebert,et al.  Structuring Feature Space: A Non-Parametric Method for Volumetric Transfer Function Generation , 2009, IEEE Transactions on Visualization and Computer Graphics.

[17]  Wolfgang Huber,et al.  Statistical methods and software for the analysis of highthroughput reverse genetic assays using flow cytometry readouts , 2006, Genome Biology.

[18]  Paul H. C. Eilers,et al.  Enhancing scatterplots with smoothed densities , 2004, Bioinform..

[19]  Jussi Klemelä Mode Trees for Multivariate Data , 2008 .

[20]  Almir Olivette Artero,et al.  Uncovering Clusters in Crowded Parallel Coordinates Visualizations , 2004 .

[21]  Estimation of a quadratic regression functional using the sinc kernel , 2007 .

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

[23]  Frederick R. Macaulay The Whittaker-Henderson Method of Graduation , 1931 .

[24]  Edmund Taylor Whittaker On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.