Automated Topic Analysis of the Voynich Manuscript

[quimqu]

UMAP is a way to turn complex data into a 2D picture so we can see patterns. In this case, each paragraph is first turned into a set of numbers (a vector) that describe how often different words appear together, sort of its fingerprint. Those fingerprints live in a huge mathematical space (maybe hundreds of dimensions).

I've only heard a bit about UMAP and never had chance to use it or understand what it does exactly, but some cursory reading on the internet suggest that UMAP tries to preserve topology of the underlying set and that its low dimensional axes are usually meaningless. Is this correct? I'm not sure how to interpret these graphs.

It’s a sort of Principal Component Analysis (PCA) space reduction, but with a very different philosophy. PCA looks for straight lines that explain most of the overall variation in the data: it’s linear and global. UMAP, on the other hand, tries to preserve the local relationships between points. It builds a kind of graph of “who is close to whom” in the high-dimensional space and then tries to project that structure into two dimensions while keeping those neighborhood relations as intact as possible.

So yes, you’re right, the actual numeric values of the UMAP axes don’t mean anything by themselves. The shape and distances do mean something: points that are close together in the plot are similar in the original space, and those far apart are dissimilar. It’s more about the geometry and continuity than the axes.

That’s why, in natural language data, you normally get cloud-like clusters (similar topics grouped together), but in the Voynich, the result is very different: the points form continuous lines. That suggests that each paragraph is most similar to the next and previous one, like a chain or trajectory.

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 In other words, the text seems to follow a very regular pattern, where nearby paragraphs (in terms of UMAP) share nearly the same word combinations. This is amazing.

Indeed!

However the sequence cannot be the current page sequence as defined by the folio numbers.  That must be the "true" page sequence.  

Many years ago I created You are not allowed to view links. Register or Login to view. but connected the dots in the "official" page order, and the result was a rat's nest for each section.  

All the best, --stolfi

Absolutelly not. It is not the folio or paragraph sequence. I will try to work to find that sequence.