Bertin Matrices: Permutations
[Bertin 1977, p.5]
And of course the hotel director becomes successful.
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.