I'm going to explain how I go about reading an academic paper because a lot of people I talk to don't read them, although that's where the best machine learning ideas are.

Michael Jordan is a Berkeley professor I follow and try to read as much as possible of. On his website is the paper, "A Flexible and Efficient Algorithm for Regularized Fisher Discriminant Analysis".

Fisher/linear discriminant analysis (LDA) is an algorithm for doing multi-class classification. A three "class" problem, for example, would be predicting whether to buy, short, or do nothing.

At least skim the paper before reading the rest of this note. I like this one because they don't leave out any steps and the matrix algebra makes it easy to write in Matlab.

So first I read over the paper about 1.5 times taking notes. Then I walked over to one of my friends at work to ask what he thought of the paper. He didn't have any opinion on it at first.

Then I opened up Matlab to implement Algorithm 1 on page 8. Here's the code. It's as straightforward as possible; First I initialize all variables, then calculate the algorithm step-by-step; Where a line is based on an equation, the equation number is given to the right in a comment, ex. %(15); And all variables have the exact same names as in the paper, so you can easily match them back and forth.

Next I wrote Algorithm 2 on page 9. Here's the code. As in the previous, the comments in the code should make it extremely clear how it relates to the paper.

The code seemed to work, so I emailed the main author, Zhihua Zhang, for his version to check mine against. Here's his code. It turns out both of his algorithms were the same, with one variable renamed. His is harder to connect to the paper itself because he uses different variable names.

My friend at work wrote the best version. It's the fastest and clearer than mine. Here's his code. He's a Matlab hacker and math Ph.D so he recognized that centering X and calculating psuedo-inverses could be sped up a lot, among other things.

In the end, all of our versions gave the same results. The third version is the most efficient. Multiclass kernel LDA is pretty good algorithm and implementing the paper directly was a fun exercise. Hopefully you can look at my version to see how to go directly from the paper to code, and then my friend's to see how to make it much more efficient.