How to calculate the Discrimination Index of a PCA?

[#1]

I need to calculate the Discrimination index of my PCA in JMP. The DI is the area between the replicates of each sample (three), divided by the total area between all the samples (six) on the PCA (see below). I know how to get a PCA on JMP but am not sure how to quantify the area between replicates and samples. Is there a way to get the DI through the menus, or would it have to be a script? 

[#2]

Hi @Mcc99 : Appears to be some proprietary thing  Alpha MOS does, as I see no references in any of the articles (that I found) that mention it, or on their website. Good luck!

https://www.sciencedirect.com/science/article/pii/S0022030218300213#bbib1

file:///C:/Users/m290593/Downloads/document_542136.pdf

https://www.alpha-mos.com/

[#3]

I wonder if there is a way I could write a script for it? 

[#4]

Hi @Mcc99 ; Yup, probably could be calculated via script etc. I've never heard of it (then again, there are loads things I've never heard of!), and I can't find anything about it the public domain; so it seems unless you can find out how Alpha MOS calculates it, it will be challenging (at best). Have you found the details of how it is calculated, what assumptions there are, etc?

[#5]

Yes, their software does it automatically, but the math seems quite simple. I'm just not sure how to find the area between points on the PCA in JMP. 

[#6]

Hi @Mcc99   Yeah, conceptually it is easy. Agreed. But is each area based on some oval-ish region around each group, or is it a based on connecting the outermost points from each group and calculating the area of the resulting polygon, or some other way? It appears you have the software (?). Is there any detail in the help documentation? If not, you will have to decide how you want to calculate areas based on what kind of geometry you are assuming. And that can be done in theory…but, in practice it may be difficult; that said, there may be some way to script it in JMP, but I’ll have to leave that to the JSL experts here.