I have been using scikit-learn's LDA implementation to do some experiments, and recently wanted to test out some modifications to the LDA derivation. I was looking at the Python implementation that scikit-learn uses, and it was nearly unrecognizable given that I'm used to seeing LDA as maximizing the scatter between classes over the scatter within classes, formulated as an eigenvalue equation.
The source code for scikit-learn LDA is https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/lda.py
Is there an implementation of LDA out there in Python that might be more recognizable to me? i.e. it uses something more like http://www.ics.uci.edu/~welling/classnotes/papers_class/Fisher-LDA.pdf