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A regularized singular value decomposition is one of the most powerful machine learning algorithms available. Two decent open source implementations are SciPy (http://www.scipy.org/) and SVDLIBC (http://tedlab.mit.edu/~dr/svdlibc/).

Timely Development also posted the full c++ code they used for the Netflix Prize http://www.timelydevelopment.com/demos/NetflixPrize.aspx




SVDLIBC's fastest sparse matrix algorithm uses Lanczos, which is still not good enough for large data sets.

Of particular interest to web scale projects would be incremental SVD methods that enable online updates to the SVD. http://www.merl.com/publications/TR2006-059/

There's also been research in academic circles regarding the use of the much more efficient (though nondeterministic) CUR decomposition in the areas of network analysis and collaborative filtering.




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