It’s been more than a week since my last post, and I hate to disappear for very long, so let me do what comes naturally: talk about myself.
More precisely, talk about what I’ve been doing.
PCA / FA
I haven’t quit playing with it. There are a few irons in the fire. The most interesting one is working thru Basilevsky. There is no electronic data for the book, but The binding of the book and its margins lend themselves to scanning, so getting his data into the computer is pretty easy, and, as usual, I enjoy doing calculations and getting answers. This is fun.
Unfortunately, his notation is a bit challenging: not only is it different from what I’m used to, but he seems to change it between sections of the book! He’s also done a few surprising things: e.g. I’m pretty sure that he normalized the rows of the A matrix, where .
Not only do I want to keep playing with his examples for the fun of it, I want to make sure of the things that surprised me.
Before that, I was trying to work out what I call classical factor analysis. Instead of a multiplicative model (whether it’s Harman and Bartholomew’s Z = AF or Jolliffe and Malinowski’s D = RC), we consider an additive model Z = AF + UY.
It is fraught with peril. I still hope to present an informative example, but we run into a foundational problem. It’s no accident that data is hard to come by in factor analysis; I quote Harman, p. 25: “The observed correlations among the variables constitute the primary data.”
Nobody but me wants to know what F is; all they want is A and U, and they get those from the correlation matrix and they’re in no hurry to work out F and Y.
Well, Harman finally talks about getting F – in the last chapter of the book. I’ll get to it, but it’s more fun to work Basilevsky first.
Before that (i.e. what I bailed on in order to wok on classical factor analysis), I was re-doing the examples on the blog. I know a lot more than I did when I first worked them out. Would I change anything? Would I say anything new? Would I modify my current plan of attack?
So far I’ve only done the Harman example. As much as I like working things out, I’m not that fond of working them out again. I’ll get back to this, when my sense of duty overwhelms my sense of adventure.
Finally, I am intrigued by the possibility of finishing off PCA by going back to my notes and looking at the questions I asked when I first started. I may end up being too embarrassed to publish them, but I think it might be an interesting and informative pedagogical activity.
Surfaces / Topology
As you can guess from the recent posts, I’ve been trying to finish off chapter 3 of Bloch. Well, trying to summarize it has lead to a lot of questions, and a lot of browsing thru other books. In terms of getting posts out, this is counter productive, but in terms of learning, it’s the name of the game.
This is what I’ve been doing almost exclusively, surfaces and manifolds.
I’ve acquired several more books (surfaces, 4D manifolds, piecewise-linear structure, and algebraic topology) that look worth adding to the bibliography, but I’m only really ready to summarize two or three of them.
I’d also like to add books on differential topology; again, I’m not ready to say very much useful about them.
I really ought to put out some elementary posts (qualitative and quantitative) about color. But that requires a bibliography first. And that’s harder than writing about color!
I have understood, and can derive, some really neat equations related to Euler angle decompositions. It might only be two posts, and I just need to write these up.
This was the stumbling block in aircraft control, so I can pick that up again as soon as I get these posts out.
I’ve also been doing some calculations about how much energy one can expect to get from solar panels on a roof. Since I don’t do that professionally – i.e. I don’ have any real experience to rely on – I’m trying to be very careful about sanity checks on the results. I’m still figuring out how to present everything I want to see.
I don’t remember what got me going on these again, but for some reason I ordered a few more books on wavelets. One of them has lead me to think that some of the calculations are far simpler than what I have done in the past (i.e. about as simple as I once thought they should have been!), and I’m looking forward to confirming that.