It is the final hours over at the Intrade’s Oscar Prediction Market. While many of the categories are runaways, the race for Best Picture is tightening. Will Avatar (click here for chart) or The Hurt Locker (click here or above for chart) prevail? Watch tonight to find out ….
Last summer, Dan, Jon and I wrote our conference paper for ASNA 2009 entitled On the Stability of Community Detection Algorithms on Longitudinal Citation Data. The purpose of this paper was to experimentally explore a number of properties of community detection algorithms, especially as applied to citation networks (c.f. Supreme Court, Tax Court, United States Code).
The model is a fairly simple discrete-time directed growing graph. At time 0, we create a completely disconnected graph with some initial number of vertices. The number of new vertices after time 0 is then modeled by a homogeneous Poisson process. For each of these new vertices, we also model the number of edges per vertex as IID Poisson distributions. The probability distribution over these edges is specified by a modified preferential attachment mechanism.
Most of our questions consider what we’ve called the average pairwise stability. This can be thought of as answering the following question: “what is the probability that Alice and Bob are friends tomorrow if they were friends today?” Here, friendship corresponds to sharing the same community. By asking this question for all pairs of vertices (dyads) for all time steps in which both vertices existed, we get a probability that a community dyad is preserved from step to step. It is important to note that we’re not claiming all algorithms applied to all systems should have high average pairwise stability. In fact, for systems that involve dynamics like random rewiring, the only way to get high pairwise stability is to put all vertices in the same community or their own community at all steps – obviously trivial and unhelpful solutions in practice.
Given this model and this conception of stability, we want to perform the following experiments:
- How do the edge-betweenness, fast greedy, and leading eigenvector community detection algorithms compare in terms of their average pairwise stability…
- for varying levels of preferential attachment?
- for varying vertex and edge rates?
- Is there a significant tradeoff between the number of communities and the average pairwise stability of these community detection algorithms?
The answers are yes, yes, and yes! You should read the paper for more details.
I’ve also produced some code to help you assess the average pairwise stability for your dataset. The code requires igraph and is only in Python at this point due to an issue with R’s vertex label handling (which I can hopefully work around). You can get the average pairwise stability methods on github and check out the example below:
Another in the series of talks at TED 2010 …. From the description … “Gary Flake demos Pivot, a new way to browse and arrange massive amounts of images and data online. Built on breakthrough Seadragon technology, it enables spectacular zooms in and out of web databases, and the discovery of patterns and links invisible in standard web browsing.”
The cover story of this week’s Economist is entitled The Data Deluge. This is, of course, a favorite topic of the hosts of this blog. While a number of folks have already highlighted this trend, we are happy to see a mainstream outlet such the Economist reporting on the era of big data. Indeed, the convergence of rapidly increasing computing power, and decreasing data storage costs, on one side, and large scale data collection and digitization on the other … has already impacted practices in the business, government and scientific communities. There is ample reason to believe that more is on the way.
In our estimation, for the particular class of questions for which data is available, two major implications of the deluge are worth reiterating: (1) no need to make assumptions about the asymptotic performance of a particular sampling frames when population level data is readily available; and (2) what statistical sampling was to the 20th century, data filtering may very well be to the 21st ….