IPIAC

1. IPIAC Multidimensional data processing

2. Parallel Coordinates • orthogonal system uses up the plane very fast • geometrical transformation • unlike the before mentioned methods • has other uses, than just visualization • low representational complexity – scatter plot array has • equidistant parallel axes • same positive orientation • each one has different scale – no normalization is performed • values need not to be numeric

4. Fundamental duality • point-line duality • a point in is represented by a (polygonal) line in projective plane • a line in is represented by a point in projective plane • is defined by • is distance between parallel axes, directed, but otherwise arbitrary • for the line is parallel with slope • a plane in is represented by lines

5. Fundamental duality x1G x2G [x1G, x2G]

6. Fundamental duality

7. Still fundamental duality

8. Still fundamental duality

9. ||-coords properties • designed to take advantage of human pattern recognition abilities • when exploring dataset with M items, there are possible subsets • any of which may be interesting • each variable is treated uniformly • no theoretical/conceptual limit • requires interactivity • no filtering and/or projection is applied • projection may hide information

10. Query types – pinch • select intervals of different variables • combine the limiting intervals together • look for • holes, peaks, valleys, gaps • density variations • regularities and irregularities • interesting for negative correlations

11. Query types – angle query • select lines with a given angle in ||-coords space • point lies • between for , → negative correlation • right to for → positive correlation • left to for → positive correlation

12. Variable order • unfortunately ||-coords are dependent on the ordering of variables • unlike with scatter plots combinations, only adjacent combinations need to be tested • represented a by a Hamiltonian path • N = 2M (even) or N = 2M + 1 (odd) permutations are required • that is, the number of combinations which need to be tested is

13. Variable combinations

14. Parallel coordinates • uses different geometry • needs a mind shift • data mining • offers much more than just data mining

15. Good visualizations • preserve information – dataset may be fully reconstructed from the visualization • reveal multivariate relations • treat each variable uniformly • are not limited by number of dimensions • have low complexity – low computational cost of constructing the visualization • are invariant to translation, rotation and scaling • have mathematical/algorithmic background – ensure unambiguity

29. Sparkline (2004) • typically small intense line chart • without axes, coordinates, frames • shows only important information (trend) • word-sized, graphic is no longer separated from text

30. Gapminder (2005) • originally moving bubble chart • moving bar chart • moving line chart • designed to show variable changes over time • acquired by Google in 2007 • available as Google Motion Chart • part of Google Chart Tools • https://google-developers.appspot.com/chart/ • http://www.gapminder.org/

31. Conclusion • visualizations are no longer passive images • interactivity enable us tocreate completely new types of visualizations • it’s not just mouse-over text • it is still important to maintain properties of good visualizations • otherwise it may become useless • although visually pleasant • is pie chart dead?