How to notice unusual news activity

Suppose you were able keep track of the news mentions of different entities, like say "Steve Jobs" and "Steve Ballmer".

What are ways that could you tell whether the amount of mentions per entity per a given time period was unusual relative to their normal degree of frequency of appearance?

I imagine that for a more popular person like Steve Jobs an increase of like 50% might be unusual (an increase of 1000 to 1500), while for a relatively unknown CEO an increase of 1000% for a given day could be possible (an increase of 2 to 200). If you didn't have a way of scaling that your unusualness index could be dominated by unheard-ofs getting their 15 minutes of fame.

update: To make it clearer, it's assumed that you are already able to get a continuous news stream and identify entities in each news item and store al开发者_如何转开发l of this in a relational data store.

You could use a rolling average. This is how a lot of stock trackers work. By tracking the last n data points, you could see if this change was a substantial change outside of their usual variance.

You could also try some normalization -- one very simple one would be that each category has a total number of mentions (m), a percent change from the last time period (δ), and then some normalized value (z) where z = m * δ. Lets look at the table below (m0 is the previous value of m) :

Name                m    m0    δ    z
Steve Jobs       4950  4500    .10      495
Steve Ballmer     400   300    .33      132
Larry Ellison      50    10    4.0      400
Andy Nobody        50    40    .20      10

Here, a 400% change for unknown Larry Ellison results in a z value of 400, a 10% change for the much better known Steve Jobs is 495, and my spike of 20% is still a low 10. You could tweak this algorithm depending on what you feel are good weights, or use standard deviation or the rolling average to find if this is far away from their "expected" results.

• Create a database and keep a history of stories with a time stamp. You then have a history of stories over time of each category of news item you're monitoring.
• Periodically calculate the number of stories per unit of time (you choose the unit).
• Test if the current value is more than X standard deviations away from the historical data.

Some data will be more volatile than others so you may need to adjust X appropriately. X=1 is a reasonable starting point

Way over simplified- store people's names and the amount of articles created in the past 24 hours with their name involved. Compare to historical data.

Real life- If you're trying to dynamically pick out people's names, how would you go about doing that? Searching through articles how do you grab names? Once you grab a new name, do you search for all articles for him? How do you separate out Steve Jobs from Apple from Steve Jobs the new star running back that is generating a lot of articles?

If you're looking for simplicity, create a table with 50 people's names that you actually insert. Every day at midnight, have your program run a quick google query for past 24 hours and store the number of results. There are a lot of variables in this though that we're not accounting for.

The method you use is going to depend on the distribution of the counts for each person. My hunch is that they are not going to be normally distributed, which means that some of the standard approaches to longitudinal data might not be appropriate - especially for the small-fry, unknown CEOs you mention, who will have data that are very much non-continuous.

I'm really not well-versed enough in longitudinal methods to give you a solid answer here, but here's what I'd probably do if you locked me in a room to implement this right now:

1. Dig up a bunch of past data. Hard to say how much you'd need, but I would basically go until it gets computationally insane or the timeline gets unrealistic (not expecting Steve Jobs references from the 1930s).

2. In preparation for creating a simulated "probability distribution" of sorts (I'm using terms loosely here), more recent data needs to be weighted more than past data - e.g., a thousand years from now, hearing one mention of (this) Steve Jobs might be considered a noteworthy event, so you wouldn't want to be using expected counts from today (Andy's rolling mean is using this same principle). For each count (day) in your database, create a sampling probability that decays over time. Yesterday is the most relevant datum and should be sampled frequently; 30 years ago should not.

3. Sample out of that dataset using the weights and with replacement (i.e., same datum can be sampled more than once). How many draws you make depends on the data, how many people you're tracking, how good your hardware is, etc. More is better.

4. Compare your actual count of stories for the day in question to that distribution. What percent of the simulated counts lie above your real count? That's roughly (god don't let any economists look at this) the probability of your real count or a larger one happening on that day. Now you decide what's relevant - 5% is the norm, but it's an arbitrary, stupid norm. Just browse your results for awhile and see what seems relevant to you. The end.

Here's what sucks about this method: there's no trend in it. If Steve Jobs had 15,000 a week ago, 2000 three days ago, and 300 yesterday, there's a clear downward trend. But the method outlined above can only account for that by reducing the weights for the older data; it has no way to project that trend forward. It assumes that the process is basically stationary - that there's no real change going on over time, just more and less probable events from the same random process.

Anyway, if you have the patience and willpower, check into some real statistics. You could look into multilevel models (each day is a repeated measure nested within an individual), for example. Just beware of your parametric assumptions... mention counts, especially on the small end, are not going to be normal. If they fit a parametric distribution at all, it would be in the Poisson family: the Poisson itself (good luck), the overdispersed Poisson (aka negative binomial), or the zero-inflated Poisson (quite likely for your small-fry, no chance for Steve).

Awesome question, at any rate. Lend your support to the statistics StackExchange site, and once it's up you'll be able to get a much better answer than this.