NIPALS and non-orthogonal components

Hi guys,

Thanks a lot for your hard work with mixomics. I ran your example on imputation through NIPALS and get several warnings for non-orthogonal components, would appreciate hearing your comments on this. I am also wondering if you could consider adding the Gram-Schmidt method for avoiding loss of orthogonality?

As the NIPALs algorithm iterates, generating each component, there are floating point errors. These accumulate and result in the components becoming non-orthogonal. While this non-orthogonality is something that you should definitely be aware of (hence the warnings), it is not inherently a bad thing. Depending on your analysis, this may not be a problem at all. For instance, the components produced via the PLS algorithm are non-orthogonal.

Your idea of including the Gram-Schmidt Process of orthonormalisation is a great one! I’ll add it on the list of enhancements but I wouldn’t expect I could get to it for some time - a lot to do a few of us to get it all done.

Thanks for the suggestion and let us know if there’s any help you need with the use of mixOmics

Max