# Updating the singular value decomposition

by using $\mathbf U$, $\mathbf S$, and $\mathbf V$), without recalculating SVD from scratch? Fast online SVD revisions for lightweight recommender systems by Brand is an accessible first paper.

I have not seen something for SVD already implemented in R unfortunately.

In short, almost all my progress since my last post has been due to other people. ) not in the database, tell me what the Rating would be--that is, predict how the given User would rate the given Movie.

In the meantime I've implemented a handful of failed attempts at improving the performance, plus one or two minorly successful ones which I'll get to. I'm tempted to get all philosophical on my soap box here and go into ways of thinking about this stuff and modeling vs function mapping approaches, yadda yadda, but I know you all are just here for the math, so I'll save that for the next hapless hosteler who asks me what I do for a living.

The basic of this update are dictated by the Sherman-Morrison formula.. \begin A^* = A - UV^T \end the Woodbury formula comes into play.

For this package to work only Numpy, Scipy and Matplotlib are required. However, Scipy need to be compiled from sources in order to use some LAPACK function "dlasd4" which are not exposed originally.

Note also that this means you are only given values for one in eighty five of the cells. Netflix has then posed a "quiz" which consists of a bunch of question marks plopped into previously blank slots, and your job is to fill in best-guess ratings in their place.

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Let $A$ be a symmetric matrix with eigenvalue decomposition $UDU^T$. Has anything similar been done for the case where the update is of the form $A B$, where $B=uv^t vu^t$ is a rank-two symmetric matrix (note we can't just do two rank-one symmetric updates)?

have shown that given such an $A$, the eigenvalue decomposition of $A \rho xx^t$ may be computed efficiently.

What if we relaxed the insistence that $B$ be symmetric and asked instead for an efficient computation of the SVD of the update $A B$?

References or thoughts would be greatly appreciated.