Just to use it as an example, StackOverflow users already associated tags to questions for a lot of questions.
Is there a .NET machine learning library that could use this historic data to 'learn' how to associate tags to newly created questions and suggest them to the user?
I made a machine learning library that might help: http://machine.codeplex.com. Its basic premise is that you can use simple lists of POCO objects and create models from them by annotating the classes. Hope this helps!
--- Update I've since moved the project here: http://numl.net.
There is a .NET library for popular statistical computing engine, R Project. The library is called R.NET.
WEKA, the data mining tool for Java, mentions several possibilities to use the library with .NET. However, it's not ported or a wrapper but bridging the communication between .NET and Java.
This looks similar to spam filtering, but with more buckets.
A widely used technique for spam filtering is Bayesian filters. A Google search will give you a lot of options, including the first hit on CodeProject.
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