AMS Feature Column: Singular Value Decomposition

A regularized singular value decomposition is one of the most powerful machine learning algorithms available. Two decent open source implementations are SciPy (<a href="http://www.scipy.org/" rel="nofollow">http://www.scipy.org/</a>) and SVDLIBC (<a href="http://tedlab.mit.edu/~dr/svdlibc/" rel="nofollow">http://tedlab.mit.edu/~dr/svdlibc/</a>).<p>Timely Development also posted the full c++ code they used for the Netflix Prize <a href="http://www.timelydevelopment.com/demos/NetflixPrize.aspx" rel="nofollow">http://www.timelydevelopment.com/demos/NetflixPrize.aspx</a>

Related to the Netflix prize, take a look at the Hodge decomposition: <a href="http://arxiv.org/abs/0811.1067" rel="nofollow">http://arxiv.org/abs/0811.1067</a>.

SVD also has an interesting application in image compression. Here's a fairly good example.<p><a href="http://online.redwoods.cc.ca.us/instruct/darnold/LAPROJ/Fall2001/AdamDave/textwriteup.pdf" rel="nofollow">http://online.redwoods.cc.ca.us/instruct/darnold/LAPROJ/Fall...</a>

SVD is the swiss army knife of linear algebra.

Nice. This helped straighten up my idea that svd is just eigenvalues for nonsquare matricies.