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Topic: Weighted Singular Value Decomposition (Read 4064 times) |
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teekyman
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Weighted Singular Value Decomposition
« on: Aug 26th, 2008, 11:31am » |
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So although I am not a desperate information mongerer, I am running into some difficulties with my own research and am wondering if any of you guys might be able to help. At least some of you, I bet, are mathy graduate studenty researchy types, and you might know a bit about Singular Value Decomposition.
The basic idea is given an nxm matrix M, you want to find matrices U(nxn),S(nxm),V(mxm) s.t. USV = M, S is Diagonal (And the diagonal entries are in decreasing order, preferably), and U and V are orthogonal. Its useful for finding optimal low-rank approximations to larger matrices, where the approximation error is measured by the sum of the errors squared.
http://en.wikipedia.org/wiki/Singular_value_decomposition
Although there is plenty of information on the interwebs about regular singular value decomposition, I'm trying to implement some solutions to the weighted variant, where you try to minimize a weighted sum of the errors squared. This time along with a matrix M, you are also given a similiarly sized matrix W.
I've modified some SVD algorithms to try to deal with weighted SVD, but after looking around a bunch, I can't even find a reference algorithm or software package that I can test mine against. I'm doing this for a start-up company and not a university, so I don't have access to hoards and hoards of papers either :/ If any of you happen to know where I could look for any info, I would greatly appreciate it. Thanks! 
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