Adhoc rules for orientation of CA axes to facilitate comparison between software visualizations
Factorial axes directions are not defined by CA calculus, so for the same input data set axes directions can change between two different CA calculus implementations.
To help users compare their CA factorial planes between two different software CA planes visualizations, by reading planes with axes in the same directions, it would be interesting to follow adhoc rules to orient the factorial axes.
'Adhoc' means that the rules have no mathematical ground, but are only some computer based conventions established for the sole purpose of aiding computer visualization of CA results between software.
They have to be implement by software after the CA calculus and before the visualization.
If TXM implements those rules and another software implements the same rules, one can hope to get compatible CA planes visualizations by getting all axes in the same directions.
Adhoc ordered rules for orientation of CA axes to facilitate comparison between software visualizations
- for each axis, the column-point (variable) with the highest contribution to the axis must have a positive coordinate
- if several point-columns have the same (largest) contribution value, make the coordinate of the point-column with the largest cos2 to the axis positive
- if several point-columns have the same (largest) cos2 value, make positive the coordinate of the point-column with the greatest distance from the origin
- if several point-columns have the same (greater) distance to the origin, make the coordinate of the point-column with the greatest mass positive
- if several point-columns have the same (largest) mass, make positive the coordinate of the first point-column in the lexicographic order of their labels (normally, points are given different labels to differentiate them in visualizations, so this should be the last adhoc condition)
Additionnal rule (may be the first rule) : if column-points can be ordered by a variable (for example chronologically), it could be interesting to orient the axis so that the points would be ordered from left to right (or bottom to top). That is: younger (smaller) points are displayed on the left of older (bigger) points.