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Subject: Re: SVD with Missing Values
Date: Fri, 5 Dec 2008 18:46:02 +0000 (UTC)
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <ghbq7k$o5r$1@fred.mathworks.com>...
> "Samuel " <sdodson2@jhu.edu> wrote in message <ghboru$60u$1@fred.mathworks.com>...
> 
> > I was under the impression also that some form of the Lanczos method could handle missing values, but im incredibly uncertain how or if to implement that.
> 
> No Lanczos is simply a specific algorithm to compute the eigen spaces of symmetric matrix, and it can be used to compute the SVD (because SVD of M is closely related to eigen spaces of M'*M and M*M'). No more no less. It more suitable for sparse matrix.
> 
> As Peter said, those are linear algebra *tools*.
> 
> Bruno 

Depending on what type of problem you're dealing with, cross-validation might also be an option. That is, if you're trying to find A in a model like
AX = Y
where you're missing data in either X or Y. If you remove the rows and columns of X or Y where data is missing you can try to predict the missing values using what's left of your system. For prediction you could use either a principal components approach (pseudo inverse) or PLS regression (which is somewhat messier but with better predictive performance if part of X and Y are correlated, but parts of either X or Y aren't).

/JC