Discuss the limitations of Modularity optimization [one time meeting]

Modularity is a way to measure how good a particular clustering is on a graph. The higher the modularity, the more "modular" the clustering -- that is, the more dense the connections within groups, and the more sparse between groups.

Last time, we read a great paper to introduce the concept, http://arxiv.org/pdf/physics/0605087 , and played around a little with igraph in python.

We mentioned that there were a couple of problems with modularity: the modularity might not have a clear global optimum (http://arxiv.org/abs/0910.0165), and there is a resolution limit for the clustering you find (http://arxiv.org/pdf/physics/0607100v2.pdf).

We'll get together and discuss these issues, esp. in the context of these two papers! The format of these meetings is very informal. Instead of a lecture, we'll highlight some of the main ideas as a group, pick apart some of the trickier parts of the papers in a discussion, and potentially go over a little code (probably with igraph) demonstrating some of the concepts from the papers.

Recommended Prerequisites:

• Linear Algebra: While not completely necessary to understand the intuition, you can't really understand this work deeply without some background in linear algebra, at least as far as understanding eigenvectors.

• Calculus: We're talking about solving optimization problems, so you could probably get away with a solid understanding of pre-calculus, but you won't get the depth without some basic understanding of function maximization in the context of gradient ascent.