transformations prior to diversity plug in distance calculations

[Nicholas_Bokulich]

@hsapers

these are the take aways (I think):

All sound reasonable, with an amendment:

@hsapers

If PCoA on a semi-metric does not produce negative eigenvalues, it’s probably an OK representation.

From the skbio documentation/warning message, it sounds like this is rather if the negative eigenvalues are not too negative... so the magnitude matters. In skimming I could not find anything in Legendre/google to support or refute this... so it sounds like the skbio documentation proposes staring at the eigenvalues to decide just how distorted the ordination is?

@hsapers

which must include ‘Hellinger distance’ which I think would just wrap the transformation into the distance calculation

Yep, sounds like hellinger transformation --> euclidean distance == hellinger distance

Since you put together a nice summary of the conversation above, I will add a summary of open development issues related to the conversation:

1. implement NMDS in q2-diversity
2. implement sqrt(D) or other methods to transform semi-metric dissimilarities prior to PCoA.

Have fun ordinating