1. Uncovering Clusters in Crowded Parallel Coordinates Visualizations Alimir Olivettr Artero, Maria Cristina Ferreiara de Oliveira, Haim levkowitz 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

9. S is a scaling factor.

10. Density Information The density function for a n-dimensional variable x is defined as : where d i is 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

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.