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Uncovering Clusters in Crowded Parallel Coordinates Visualizations

Uncovering Clusters in Crowded Parallel Coordinates Visualizations. Alimir Olivettr Artero , Maria Cristina Ferreiara de Oliveira, Haim levkowitz Information Visualization 2004. Abstract. The idea is inspired by traditional image processing techniques such as grayscale manipulation.

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Uncovering Clusters in Crowded Parallel Coordinates Visualizations

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  1. Uncovering Clusters in Crowded Parallel Coordinates Visualizations AlimirOlivettrArtero, Maria Cristina Ferreiara de Oliveira, Haimlevkowitz Information Visualization 2004

  2. Abstract • The idea is inspired by traditional image processing techniques such as grayscale manipulation. • Reducing visual clutter and allowing the analyst to observe relevant patterns in the parallel coordinates.

  3. Introduction • The strong overlapping of graphical markers hampers the user’s ability to identify patterns in the data when the number of records and the dimensionality of the data set are high. • It is important to avoid displaying irrelevant information and enhancing the presentation of the useful one.

  4. Introduction • Tackling this problem with a strategy that computes frequency and density information, and uses them in parallel coordinates visualizations to filter out the information to be presented to the user.

  5. Frequency Information • The frequency function for a n-dimensional variable x is defined as : where h is the size of bins, σ is the number of records in the same bin, m is the number of all records.

  6. Frequency Information • A two-dimensional matrix is generated to store the frequency of each pair of attribute values, which is then used to draw the polygonal lines for the records in the data set. • For a data set with n attributes, n-1 frequency matrices are generated, one for each pair of attributes.

  7. Frequency Information • All the non-zero matrix elements generate a line segment in the visualization and the pixel intensity used to draw the line segment. • Each line segment is drawn with the Bresenham algorithm:

  8. Interactive Parallel Coordinates Frequency and Density plots • The intensity of the pixel with coordinates (q,p) is given by: • Square wave smoothing filter is used for each pixel:

  9. Interactive Parallel Coordinates Frequency and Density plots • S is a scaling factor.

  10. Density Information • The density function for a n-dimensional variable x is defined as : where diis the i-th record of the data set and K is the kernel function, the parameter defines a smoothing factor or bandwidth.

  11. visualizations of the Pollen data a) Frequency Plot b) Density Plot

  12. Interactive high-dimensional clustering with IPC plot

  13. Interactive high-dimensional clustering with IPC plot

  14. Interactive high-dimensional clustering with IPC plot

  15. Interactive high-dimensional clustering with IPC plot

  16. Interactive high-dimensional clustering with IPC plot

  17. Performance • Running times in seconds for the proposed algorithm with different values of m and n.

  18. Conclusions • The new plots support interactive data exploration of large and high-dimensional data sets, allowing users to remove noise and highlight areas with high concentration of data. • The proposed algorithms use only integer arithmetic to compute the frequency matrices.

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