G. Sawitzki StatLab Heidelberg Last revision: 2014-04-19 by gs

Bertin Matrices: Permutations

Ce point est fondamental. C’est la mobilité interne de l’image qui charactérise la graphique moderne.
[Bertin 1977, p.5]
Hotel orig
Hotel occupancy data (orig.)
J. Bertin uses a small data set on hotel occupancy data to illustrate his ideas, and tells a story: a hotel director finds a way to represent his occupancy data as a matrix, rearranges it, and gets important information from this new look at the rearranged data. Relations become obvious in the rearranged matrix.
And of course the hotel director becomes successful.
Hotel rearranged
Hotel occupancy data (variables rearranged)


With a matrix layout, rearrangement is specified by possible permutations of rows and of columns.

In an interactive environment, this can be done by dragging variables and/or cases to a new place.

This may also be done using commands for rearranging or sorting.
The criteria for rearrangement may be related to information used in the first two steps, matrix adjustment and setting attributes, but it should be considered an independent step.

Various seriation methods may apply. This is where Bertin's ideas about ``internal mobility'' as a characteristics of modern graphics come to action. The typical situation is to select scores and display attributes, and then search for optimal or good seriations. The arrangement often leads to hard optimisation problems. Placing this step later allows to use information from score transformation and attributes, which may allow more efficient algorithms.

In the end, we may be better with a good solution which helps to solve the practical problem, instead of an optimal solution to a theoretical one. These may differ considerably.