Is discriminant analysis supervised learning?

Question

Is linear discriminant analysis, specifically Linear Programming Discriminant Analysis (LPDA), supervised learning? Can you provide a valid reference that states so if possible.

My study supervisor and I have been disagreeing about it. I'm convinced linear discriminant analysis, whether Fisher LDA or LPDA, is supervised learning. Both techniques use a labelled set of objects to derive a function which can be used to predict class labels for unlabelled objects.

My study supervisor does not agree, stating that nothing is "learned" when using discriminant analysis.

Answer 1

As you say, LDA is supervised. How does your supervisor define "learning"?

But yes, usually it is counted as supervised learning. Reference, e.g. first 2 pages of The Elements of Statistical Learning

• You can use LDA models for prediction of new cases. (I'd say that implies that something has been learned
• However, you can also put emphasis on the projection aspect, which may be used in a descriptive rather than a predictive way.

I think we wrote something here.