Happenings Apr 25

I thought about trying to put this post out last evening and last night, but I have a huge backlog of unread magazines, so I spent part of the evening reading in my recliner. I also record several crime shows during the week ( NCIS, all three CSI, Numb3rs, Bones, and Criminal Minds), and watch them on weekend evenings. That cuts down on channel surfing, and I can skip commercials. I did that after reading. Actually, I watched Numb3rs in real time, and read magazines during the commercials. About 11:30 PM I briefly considered working on this draft.

So, as usual, it is about noon on Saturday as I begin this post. I have already written in my journal, and I have done my playing around with whatever mathematics the kid in me wanted to do this morning.

Algebra. Read the rest of this entry »

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Wavelets: The D4 scaling function

Introduction

I am going to do something a little risky. I’m going to show you how to approximate a particular function – the Daubechies D4 scaling function – even though I am a little shaky on the justification.

If you have ever looked at wavelets, you have probably seen this picture. It is a quintessential “father wavelet” – more commonly, I think, called a “scaling function”.

d4-1-dwg8

I want to compute it; this is not relevant to computing wavelet coefficients, because just as this is computed from its definition, so wavelet coefficients which depend on it and its associated wavelets are computed from its definition rather than from its values.

Talking about this is much like talking about one of one’s favorite movies: what makes something one of my favorite movies is deeply personal, and it doesn’t usually affect my friends that way. To them, at best, it’s just another movie; at worst, they think it is a dud. Read the rest of this entry »

the other form of greek phi?

I have no idea how to access the following symbol
picture-32

in latex for wordpress. I will need the alternative \phi for other purposes in related posts, so i do not wish to use it instead.

Does anyone know the answer?

Happenings Apr 18

Once again it is about noon on Saturday. Not a whole lot has changed in a week. I am still planning to spend the weekend on wavelets.

Last weekend and this one have been different from my usual practice. I did not look at what was on my plate — my to-do list for math and blogging — at all last weekend, and I probably won’t look at it this weekend. Usually I am playing around with a few different kinds of mathematics, and a few choices of posts to put out here, so I keep looking at what things I might do.
Read the rest of this entry »

Happenings Apr 11

Okay, it’s just after noon on Saturday. I have continued working with wavelets, but I have to tell you I’m not happy. So far, no single book I own seems to be answering all of my questions.

As a result, the projected wavelet bibliography is growing. And the number of details that should be mentioned for each book is growing, too.

As much as I would like to compute like a madman, I think I’m going to have to curl up in a comfortable chair and read about wavelets for a while. In several books.
Read the rest of this entry »

Happenings Apr 4

Some things are more than habit, they are personality. One year in high school I had to write an English paper every other Friday. That was a good thing: I learned to write, by writing.

What I did not learn was to write the papers ahead of time. All of those papers got written Thursday night — usually late Thursday night.

Now it’s 7:37 AM Saturday morning and I have about 35 minutes to put out this post.

Some friends and I are getting together to watch “The Lord of the Rings”.
Read the rest of this entry »

PCA / FA. A Map to my posts

The Posts

The purpose of this post is to provide guidance to a reader who has just discovered that I have a large pile of posts about principal components / factor analysis. This pile of posts might seem a very jungle, without any map.

Here, have a map.

As I finalize this post, it will be number 52 in PCA / FA. Here’s a list of the 52 posts, including the dates spanned by any group, and the number of posts in that group. (When the picture was taken, I didn’t know when this would be published. In fact, post 51 was scheduled but not yet published. Even more, post 51 did not even exist when the first picture was created.)

posts-table
transition/attitude matrices is a post that is sometimes relevant when we discuss “new data” in PCA, but it is not in the PCA / FA category.

“tricky prepro” is short for “tricky preprocessing”, and discusses the combination of constant row sums and covariance or correlation matrix.
Read the rest of this entry »