Literature on discriminant analysis

Question

Can anyone suggest a good book on discriminant analysis - comprehensible and detailed? (Kendall and Stuart write about the subject too concisely.)

Thanks in advance.

Answer 1

Extended comment:

Linear discriminant analysis is a topic in 'multivariate analysis'. If you google that topic for 'books' you will see, among other things, a couple of pages on our associated site 'crossvalidated' dealing with recommendations of books in the field. Take a look to see which ones contain chapters on 'discriminant analysis'.

Modern books on multivariate statistics do not seem to focus as much on discriminant analysis as older ones did. 'Cluster analysis' is not exactly the same thing, but a related topic. Maybe your first task is to find out if there is a related topic in multivariate analysis that is of equal or greater interest to you. Perhaps with online datasets and modern software to match.

Discriminant analysis was invented by R.A. Fisher. He illustrated the key ideas with his now-famous dataset on iris flowers: petal and sepal lengths and widths for three species of irises. The question is whether it is possible to DISCRIMINATE among the three species using only these four measurements. That is NOT just asking whether, for example, data indicate that sepal widths have different species population means. It is asking whether the sepal widths differ enough that you can identify which of the three species a particular flower belongs to just knowing its sepal width. (The answer is NO, but if you consider all four measurements in 4-space, you can almost make an ID without error.)

Given the computational limitation of his time (1920s, I believe), Fisher took some shortcuts. It might be a worthwhile (although certainly not original) senior project to do a modern discriminant analysis of the iris data using R or some other statistical package. The iris dataset is of moderate size and has no missing data--as you specified.

Some years ago I published a book 'Learning Statistics with Real Data' in which one chapter used an older version of Minitab to do a somewhat more modern discriminant analysis of the iris data than Fisher's. (I say 'somewhat', because the Minitab procedure available then made some assumptions that aren't quite true.) The book is out of print (used copies on Amazon for \$5-\$10), but if you google my faculty profile to get my contact info, I can email you a .pdf of the chapter.

There is an inexpensive Google-Sage book on discriminant analysis by Klecka (1980) with editorial collaborators I know. But I have not looked at it. Given the date, I do not suppose you will get much help there with computation or large datasets, but it might be a good orientation.

I also noticed there is a You Tube demo on discriminant analysis using R. At least the price is right.

The modern computationally oriented books I have seen on discriminant analysis seem to assume you already know what it is and just want to know how to run a particular computer program.

Your faculty adviser should give you some guidance as to the subject and level of your project. Statistics, linear algebra, graphics, and computation all play roles in discriminant analysis. I won't make specific recommendations because I don't know enough of your background, requirements of such a project, or your enthusiasm for getting into unfamiliar territory.