This is a follow-up question to Is PCA appropriate for comparing subsets of panel data?.
It turns out that, yes, PCA is appropriate. But there are also many other ways to reduce n-dimensional data to 1-3 dimensions that can be visualized, and I'm having trouble getting a global view of the available set of techniques for doing so. For instance, several are mentioned in this question and this question. The latter question has a link to Nonlinear Dimensionality Reduction on Wikipedia, which is relatively comprehensive, even encyclopedic, for a Wikipedia article on a technical subject. But it's still Wikipedia and I'd like to have everything in one place. edit: there's also this question from today.
Is there a somewhat-comprehensive reference for dimension reduction? For instance, I'd really like an explanation of why the "manifold-based" approaches (e.g. ISOMAP) are different or better than distance-based approaches (e.g. classical MDS). Ideally it would include some treatment of different distance metrics as well. Ultimately I'm trying to get a handle on the kinds of questions each technique is designed to answer.
Obviously this could turn out to be a bigger subject than I realize. I'm aware that, e.g., self-organizing maps are a type of neural network, and neural networks are quite different "under the hood" from, say, multidimensional scaling. I'm hoping that a reference or set of references exists that doesn't require me to know the gory underlying details of each approach. Learning everything there is to know about statistics is a long process and I'm not quite there yet (although I'm making good progress, in part thanks to this site).