Multidimensional data processing. x 1G [x 1G, x 2G ] x 2G.
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Transcript of Multidimensional data processing. x 1G [x 1G, x 2G ] x 2G.
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
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
||-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
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
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
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
Parallel coordinates
• uses different geometry• needs a mind shift• data mining• offers much more than
just data mining
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
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
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/
Conclusion
• visualizations are no longer passive images • interactivity enable us to create 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?