[split] Does Voynichese evolve from A to B?

[Jorge_Stolfi]

But what is the fitting algorithm, exactly?

The initial version used a parameterized curve with cubic splines, eleven knots and a smoothing penalty. The more complex version i introduced in the stability analysis utilized You are not allowed to view links. Register or Login to view., which yes, is intended to be used with nonlinear data.

What graph structure did you use? Just a simple path, with one vertex per Golf section, with "bristle" edges from each path vertex to the pages of that section? Did you pre-define that structure (including the assignment of pages to Golf sections), or did ElPiGraph figure it out on its own?

Note that ElPiGraph, from what I understood, does not normally determine whether the sections lie along a single curve, or in any other topology.  That is a prior assumption that is imposed when you specify the graph.

But I explained why it is very unlikely that a gradient due to time would exist in the final draft.  Like us writing any paper or book, the Author must have gone back and forth over the draft, editing and re-editing pages that he wrote previously -- and applying to them any changes of spelling or nomenclature that he may have decided to make along the way.  

But you have not really addressed the fact that the lines you drew (for the 2nd time now) splitting those groups into clusters, actually does not split them along the axis you are claiming. As you have grouped them you have:

• 1 cluster of mostly Herbal A
  
• 1 cluster of Pharma, Some herbal A, and astro
  
• 1 cluster of cosmo, f58, herbal b, and half of stars
  
• 1 cluster of the remainder of stars and Bio
  

Sorry, I though I had answered, but seems I didn't.

I can improve the yellow line on the MDS1 x MDS2 plane, that separates between the left cluster (traditional Herbal-A, Pharma, and you say Astro?; my A+B in the figure) and the right cluster (everything else, including Herbal-B; my C+D), so that at most one point from the traditional sections lies on the wrong side.
   
Surely a more definite separation between these two sets exists in R^256.  (In fact, if you have 230 data point in R^256 space, for any subset X of those points there will be a hyperplane that neatly separates X from the other points,almost certainly.)

It is not clear from this projection whether each side is a single cluster or multiple clusters.  On the left side, it does look like that the light blue, dark blue, cyan, and green dots form three compact clusters that may be separated in R^256 space but happen to overlap in this projection.  However, it may also be that even in R^256 space all those points are still one elongated cluster; and the colored subsets are just different parts of that subset that were arbitrarily sliced off it -- like the top, middle, and bottom parts of an egg.

On the other hand, I did You are not allowed to view links. Register or Login to view. decades ago, using an R^50 data space consisting of the frequencies of the most common 50 words in the whole VMS.  IIRC, in that data space, for each pair of the major sections there seemed to be a 2D projection, using the centroid-to-centroid line as one of the axes, where the two sections projected as compact well-separated clusters of page points.  Including Herbal-A and Pharma, etc.

Thus I expect that in your R^256 space too the page points will comprise 4-6 compact well-separated clusters; and I expect that each cluster will be mostly contained in one of the traditional sections.  If there are exceptional pages, that would be notable and we should examine them.

So if you think the horse shoe is really composted of these clusters, you haven't provided an explanation for why these would be grouped this way, it doesn't align with section or topic at all.

Again, there is no "horseshoe"!  

The pages of each major traditional section are definitely clustered in your R^256 data space, and maybe those clusters can be split into well-separated sub-clusters that would imply a division into sub-sections, perhaps even your Golf sub-sections.  

But those clusters do not fall along any simple curve.

And, even if they did (or if you used a sufficiently flexible curve), there is no reason to expect that the order implied by that curve would be related to time (of scribing to vellum,  of writing the final draft, of collecting the information, of the composition of the ur-books...).  Nor of the intended reading order of the sections, if there was one (which now I am fairly convinced that did never exist).  

Topic and other factors seem quite sufficient to explain the separation of sections in R^256 and their relative positions.   Except that the A/B split may be due to a comprehensive spelling reform, in which case it is likely (but still not certain) that all the A material was drafted by the Author before all the B material, or vice-versa.

All the best, --stolfi

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