Proposed Manuscript Chronology

[npcompl33t]

@npcompl33t Is the PCA data open-sourced? Could we take a peak on the MDS axes and their coordinates to try and interpret that? Sorry if you've mentioned this in your main thread, I'm having a hard time catching up on threads lately.

• I actually have created You are not allowed to view links. Register or Login to view.! 
  
• I also had open sourced You are not allowed to view links. Register or Login to view.
  

However, i did not directly publish the underlying transition or direct MDS data. So i went ahead and did that.

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I want to be clear though, I am not claiming PCA1,MDS1, or any single dimension = time. 

In fact, when a Guttman Horseshoe appears, it means you can not simply ascribe any one single MDS or PCA dimension to the dominant sequential ordering. The linear path moves through multiple PCA dimensions. This is why the Guttman horseshoe is often considered a confound to PCA analysis, because it means there is a single dominant factor that is not directly captured by any one PCA dimension. The point of fitting the curve to the data is to recover this dominant sequential ordering.

In the Flinders Petrie example, he recorded different aspects about pottery. You can imagine styles changing, perhaps necks slightly elongate for a few years, then start to slowly widen, then maybe gain fluted edges. The PCA captures all of these differences but cannot put them all on a single dimension. When David Kendall did MDS on Flinders' pot data, he noticed the same horseshoe. A single dimension did not correspond to the pottery chronology. He was able to recover the full chronology, by tracing the path across multiple dimensions, and that is what I am doing here. Kendall's work on horseshoes are literally textbook, You are not allowed to view links. Register or Login to view.. 


Another example, here is a 3D plot of the You are not allowed to view links. Register or Login to view.. You can see the horseshoe appearing. This means there is a dominant sequential ordering underlying the data. This sequence is not directly captured by any MDS dimension. It can be recovered though, which is what the plot on the right is.

   


So if a horseshoe appears, it means there is a dominant, single, continuous gradient driving the data. My hypothesis here is that it is time, as it was in Kendall's example. That is my hypothesis, and you might think it represents something else, but a single dominant gradient does exist.