How to statistically test the separation of two clusters in PCA

Question

[bright602]

Hi, I am using the dba.plotPCA function in DiffBind to get a PCA plot. Could someone tell me how to use the statistic test to test the separation between two clusters? If possible, could I add the 95% CI ellipses in dba.plotPCA function? Thanks a lot for your help!

[Ram]

What will you testing? What statement do you wish to be 95% confident about?

[bright602]

I am trying to know whether the two clusters are separated enough. Visually they are, but I just want to add some stats power. If not easily achieve, I am thinking to mark the 95% CI ellipses and illustrate the degree of overlapping/separation.

[Ram]

That's just a repeat of what you already said. 95% CI on what, exactly? For example, in a t-test, the confidence interval is for the difference in mean between the two populations being tested. A PCA is a tool to reduce dimensionality - I don't think it tests any hypotheses to give you confidence intervals.

I'm sorry - I did not understand your question well. Does this SO post help: https://stackoverflow.com/questions/13936051/adding-ellipses-to-a-principal-component-analysis-pca-plot

[bright602]

Thank you for your help.

Answer 1

[Alex Reynolds]

Some links that may be of general interest:

• https://towardsdatascience.com/gaussian-mixture-models-d13a5e915c8e

• https://en.wikipedia.org/wiki/Akaike_information_criterion

• https://en.wikipedia.org/wiki/Bayesian_information_criterion

• https://lukapopijac.github.io/gaussian-mixture-model/

• https://www.barelysignificant.com/post/aicbic/

• https://www.kaggle.com/tundraman/pca-gmm-clustering

[bright602]

Thanks a lot Alex for the links!

[Alex Reynolds]

I think there is some discussion about CIs in relation to information measures. Hope it helps.