Proposed Manuscript Chronology

[npcompl33t]

This is what is known as a Guttman horseshoe. It is a You are not allowed to view links. Register or Login to view. You are not allowed to view links. Register or Login to view.that can happen with both PCA and MDS.

This "Guttman effect" is a fancy name for the banal observation that, if you try to fit a simple arc of curve to a bunch of random points in 2 or more dimensions, the result will usually be a curved arc rather than a straight line.

There is no reason to assume that the different sections of the VMS were created by a single process (natural or mechanic) whose parameters varied gradually along a single dimension (like time).  Therefore, there is no justification for trying to fit a single curve to the clouds of points obtained from each section.  They are expected to have different statistics because of different subjects, formats, and styles.   

If cloud B happens to lie somewhat between clouds A and C in a particular projection, it does not follow that it was created after A and before C,or vice-versa.  It does not even follow that its topic is somehow "intermediate" between those of A and C.

All the best, --stolfi

Respectfully, this statement is not accurate. The Guttman effect by definition can only occur when a strong, single underlying linear gradient or sequential ordering is forced into a lower-dimensional space using linear dimension reduction techniques. Its very appearance does in fact mean there is some single underlying linear gradient in the data. You can argue that gradient does not represent time, but you can't claim that such a gradient does not exist. It very clearly does, and is a prequisite for the horseshoe shape to appear.

Similarly if the Guttman effect is present, then fitting a curve is not only justified, it is the documented correct approach to recover the underlying linear gradient or sequential ordering.