What is a good source to learn about multidimensional scaling?

Question

I don't have much experience with statistics (my education included 8 credits of pure statistics, another 8 of related subjects). I mostly learned about distributions and significance tests for distribution parameters, and a bit about linear regression. I also had some factor and component analysis, but have completely forgotten them and don't have the textbook any more. Now we have to evaluate some empirical data and the other people on our team have even less knowledge in statistics.

After looking at different methods, I think that multidimensional scaling is the right technique to use - the examples I see it used for are similar to what we want to do. I found a book about it, but I find it very hard to learn from it. First, it is not at my level - the second paragraph of the "basics" chapter starts with the words "If σ_ij is the affinity between object i and object j" and I am not sure what the affinity in my case is. Second, it is very old, from 1979, and I think there could have been improvements since then. Third, there is of course nothing about software support in this book. Fourth, it is in German, and googling about things I don't know is difficult, because there are better sources in English online, but I don't know the correct English translations of specific terms.

What I want is a better book. Here are my criteria for it.

• It should be a textbook aimed at students, not a reference tome for specialists.
• I would appreciate if it is written from an applied point of view, but it is more important for me to grasp the theory than to see a script which is supposed to spew out the result I am supposed to want.
• It won't hurt if it is a more general statistics textbook which includes a sizable section on MDS (I might need to refresh other knowledge), but please not an exhaustive brick which covers all the material for a B.Sc. in statistics and costs its weight in Euro notes.
• I would prefer it to be in English, but if the ultimative source is in another language, please tell me about it.
• I will use R for the evaluation, so if there is a book which uses R for the examples, it would be great. A book which is dependent on any tool - even if it is R - is a complete no-go (like a book which says "to obtain this result, use function X of package Y" instead of explaining the calculations which have to be made to obtain the result).

If you know of a book which meets at least the majority of these criteria, I'd love to hear about it.

Answer 1

A good textbook on multivariate data analysis, mixing introductory material and more advanced theory, is Modern Multivariate Statistical Techniques, by Alan J. Izenman (Springer, 2008). A review by John Maindonald was published in the JSS.

It features a complete chapter dedicated to MDS (chapter 13), with a lot of illustration using the open-source R statistical software. More on R packages can be found on CRAN Multivariate Task View, among others.

As an alternative, I would suggest the Handbook of Applied Multivariate Statistics and Mathematical Modeling, by Howard E. A. Tinsley and Steven D. Brown (Academic Press, 2000). Again, a complete chapter is devoted to MDS. Less mathematical background is required.

As for online reference, I can also recommend Forrest W. Young's course on Multidimensional Scaling.