I've been on hiatus for a while due to work at and studies, but I thought I'd take a quick break and post about some interesting stuff I've been playing around with, and that's spectral clustering.
I'll try to assume no previous knowledge of clustering data, so I'll give a brief introduction to that.
The post goes into the k-means clustering algorithm, spectral clustering, and a C++ implementation of both.
Recently the students for the class I TA in had to solve a couple of exercises involving the boolean satisfiability problem, also known as SAT. I'd like to talk about some aspects of it which, while by no means new, should be interesting for someone being introduced to the problem.
I had often heard the expression "C++ now has covariant return types". To be honest, I vaguely knew covariance was a mathematical term, and I was also pretty sure it had nothing to do with statistical covariance.
Now that I understand a bit more about category theory, I feel I can clarify some things about this usage of the word "covariance" in programming languages. Surprisingly, it is not a terrible bastardization of the mathematical term, as C++ and Java have done to the word "functor".
Given a graph , with , , we can define a matrix , called 's incidence matrix, defined as such:
In this post, we study some of this matrix's algebraic properties.
Given a graph , with , , we can consider the matrix defined as such:
We call this the adjacency matrix. In this article we study some of its algebraic properties.