· ranking-systems

Ranking Systems: What I've learnt so far

I often go off on massive tangents reading all about a new topic but don't record what I've read so if I go back to the topic again in the future I have to start from scratch which is quite frustrating.

In this instance after playing around with calculating the eigenvector centrality of a sub graph I learnt that this algorithm can also be used in ranking systems.

I started off by reading a paper written by James Keener about the Perron-Frobenius Theorem and the ranking of American football teams.

The Perron-Frobenius Theorem asserts the following:

a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector has strictly positive components

This is applicable for network based ranking systems as we can build up a matrix of teams, store a value representing their performance against each other, and then calculate an ordered ranking based on eigenvector centrality.

I also came across the following articles describing different network-based approaches to ranking teams/players in tennis and basketball respectively:

Unfortunately I haven't come across any corresponding code showing how to implement those algorithms so I need to do a bit more reading and figure out how to do it.

In the world of non network based ranking systems I came across 3 algorithms:

Scott Hamilton has an implementation of all these algorithms in Python which I need to play around with. He based his algorithms on a blog post written by Jeff Moser in which he explains probabilities, the Gaussian distribution, Bayesian probability and factor graphs in deciphering the TrueSkill algorithm. Moser's created a project implementing TrueSkill in C# on github.

I follow tennis and football reasonably closely so I thought I'd do a bit of reading about the main two rankings I know about there as well:

Now that I've recorded all that it's time to go and play with some of them!

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