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IPIAC

IPIAC. Multidimensional data processing. 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

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IPIAC

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  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

  3. 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

  4. Fundamental duality x1G x2G [x1G, x2G]

  5. Fundamental duality

  6. Still fundamental duality

  7. Still fundamental duality

  8. ||-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

  9. 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

  10. 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

  11. 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

  12. Variable combinations

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

  14. 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

  15. 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

  16. 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/

  17. 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?

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