Human eye has own Curse of Dimensionality (term suggested in 1961 by R.Bellman and described independently by G. Hughes in 1968). In most cases the data (before they visualized) usually organized in multidimensional Cubes (n-Cubes) and/or Data Warehouses and/or speaking more cloudy – in Data Cloud – need to be projected into less-dimensional datasets (small-dimensional Cubes, e.g. 3d-Cubes) before they can be exposed through (preferably  interactive  and  synchronized set of charts, sometimes called dashboards) 2-dimensional surface of computer monitor in form of Charts.

Projection of DataCloud to DataCubes and then to Charts

During last 200+ years people kept inventing all type of charts to be printed on paper or shown on screen, so most charts showing 2- or 3-dimensional datasets. Prof. Hans Rosling led Gapminder.org to create the web-based, animated 6-dimensional Color Bubble Motion Chart (Trendalyzer):

tumblr_mssaaxhajz1stz40uo1_500

ansd screenshot of it here:

which he used in his famous demos: http://www.gapminder.org/world/ , where 6 dimensions in this specific Chart are (almost a record for 2-dimensional chart to carry):

  • X coordinate of the Bubble = Income per person,
  • Y coordinate of the Bubble = Life expectancy,
  • Size of the Bubble = Population of the Country,
  • Color of the Bubble = Continent of the Country,
  • Name of the Bubble = Country,
  • Year = animated 6th Dimension/Parameter as time-stamp of the Bubble.

Trendalyzer was bought from Gapminder in 2007 by Google and was converted into Google Motion Chart, but Google somehow is not in rush to enter the Data Visualization (DV) market.

Dimensionality of this Motion Chart can be pushed even further to 7 dimensions (dimension as an expression of measurement without units) if we will use different Shapes (in addition to filled Circles we can use Triangles, Squares etc.) but it will be literally pushing the limit of what human eye can handle. If you will add to the consideration a tendency of DV Designers to squeeze more than one chart on a screen (how about overcrowded Dashboards with multiple synchronized interactive Charts?), we are literally approaching the limits of both human eye and human brain, regardless of the dimensionality of the Data Warehouse in backend.

Below I approximately assessed the dimensionality of datasets for some popular charts (please feel free to send me the corrections). For each Dataset and respective Chart I estimated the number of measures (usually real or integer number, can be a calculation from other dimensions of dataset), the number of attributes (in many cases they are categories, enumerations or have string as datatype) and 0 or 1 parameter (presenting a well-ordered set, like time (for time series), date, year, sequence (can be used for Data Slicing), natural, integer or real  number) and Dimensionality (the number of Dimensions) as a total number of measures, attributes and parameters in a given dataset.

Chart Measures Attributes Parameter Dimensionality
Gauge, Bullet, KPI 0 0
Monochromatic Pie 1 1
Colorful Pie 1 1 2
Bar/Column 1 1 2
Sparkline 1 1 2
Line 1 1 2
Area 1 1 2
Radar 1 1 2
Stacked Line 1 1 1 3
Multiline 1 1 1 3
Stacked Area 1 1 1 3
Overlapped Radar 1 1 1 3
Stacked Bar/Column 1 1 1 3
Heatmap 1 2 3
Combo 1 2 3
Mekko 2 1 3
Scatter (2-d set) 2 1 3
Bubble (3-d set) 3 1 4
Shaped Motion Bubble 3 1 1 5
Color Shaped Bubble 3 2 5
Color Motion Bubble 3 2 1 6
Motion Chart 3 3 1 7


The diversity of Charts and their Dimensionality adding another complexity for DV Designer: what Chart(s) choose. You can find on web some good suggestions about that. Dr. Andrew Abela created Chart Chooser Diagram

Choosing a good chart by Dr. Abela

and it was even converted into online “application“!

Permalink: http://apandre.wordpress.com/2011/03/02/dimensionality/

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