Page Clusters in the Voynich Manuscript

A Principal Component Analysis of the Voynich Manuscript Pages showed that pages form clusters in agreement with the illustrations which appear on the same pages, or lack of them. The clusters found were

1. Herbal
2. Pharmaceutical
3. Cosmological, Astronomical, and Astrological
4. Text and Recipes
5. Biological

The cluster formed by the herbal pages was larger, and overlapped the other clusters except for the one containing the biological pages. Furthermore, it contains both Currier A and B pages. It was also noted that the dividing line between Currier A and B was somewhat arbitrary.

The herbal pages were separated from the rest of the manuscript. Two text pages, f1r and f66r, are contiguous only with herbal pages and cluster similarly, so they were also included. Two other statistical techniques, minimum spanning tree and k-means clustering were then performed, to find out if there were clusters within the herbal pages. While the minimum spanning tree is unique for a given set of points, k-means clustering is something of a black art. One problem is that it is biased towards circular clusters. Usually the value of k, the number of clusters, is supplied, and the results verified visually. When run to determine k, it found a single cluster. When k was set to 2 to see if it separated Currier A and B pages, one cluster had only Currier A pages, and the other had both Currier A and B pages. When k was set to 3, the result was the similar to k=4, but with the blue and black clusters merged. The best results were obtained for k=4, when the clusters found approximately matched branches of the minimum spanning tree, but still required a few corrections. The red points correspond closely to Currier B pages.

Figure 1: PCA of herbal pages with minimum spanning tree and k=4 means clustering superimposed

I think that the red-black boundary should be between f51r and f52r, and the black-blue boundary should be between f2r and f15r. This maximizes the distances between the clusters in the spanning tree. Then, a few points should change cluster to ensure that every point in a cluster is reachable from every other point, without passing through another cluster, for example f9v should move from green to black, and f90v2, f48r, and f87v should move from red to black. This means that f48r should now be classified as Currier A, and f51r and f65v as Currier B.

The page classifications are then

K-means clustering was also done for the text/recipes pages and biological pages. The best results were for k=3, and no manual corrections were required.

Figure 2: PCA of text/recipes pages with minimum spanning tree and k=3 means clustering superimposed

Figure 3: PCA of biological pages with minimum spanning tree and k=3 means clustering superimposed

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© Copyright Donald Fisk 2017