TITLE: Does "Big Data" Have a Ramsey Theory Problem?
QUESTION [5 upvotes]: I'm erring on the side of conservatism asking here rather than MO, as it is possible this is a complex question.
"Big Data" is the Silicon Valley term for the issues surrounding the huge amounts of data being produced by the global IT structure.  Advanced mathematics is starting to pay attention to this, with very early thoughts on topological approaches.  For example, see the Wiki here.
But one obvious way to think about patterns in Big Data is as polychromatic colored complete graphs: let the vertices be your data, let the edges represent relations between data, and let the colors be specific relations (which are the objective of Big Data visualization), with some neutral color representing no relation.
By the very definition of Big Data and Ramsey Theory, this virtually guarantees the existence of monochromatic complete subgraphs which may be nothing but spurious relations that must exist because of Ramsey Theory.
I am NOT a graph theorist in any way. So what I am asking specifically is this:

Are there other techniques that can be overlayed on to a graph theoretical approach that add information that the monochromatic subgraphs are real "signal" and not Ramsey noise?  Or, am I misunderstanding, and the Ramsey structures are not actually noise?

REPLY [2 votes]: I don't know if "Big Data" has a Ramsey subgraph problem, but many, many big data practitioners have an "applied Ramsey Theory" problem.
The fundamental theorem of applied Ramsey Theory is:

Theorem: For any algorithm, if you look hard enough, and define terms loosely enough, you can find data that the algorithm fits perfectly.

This, of course, has a well-known corollary.

Corollary: For any algorithm for which you seek funding, there exists a data set that can be declared interesting enough to fill a proposal.

This phenomenon is particularly noticeable in many big data applications; semantic search is a wonderful example. Often, you find researchers that see an interesting problem but don't have the sophistication to tackle it (because the sophistication may not even yet exist). So they create frameworks, and then create problems on those frameworks, while eliding any discussion of the degree to which the framework matches reality.
Of course, they're very good at creating problems within frameworks and then solving them, but it is not yet clear that they've actually manifest progress towards any true mathematical understanding.

That said, a foundation of mathematics is understanding simpler cases to the ones that are interesting, so it may be that what's being done in the "big data" world is indeed very interesting. But I haven't seen any wonderful breakthroughs yet, despite seeing many wonderful solutions to problems that don't actually exist.