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Topic: about matrix approximation (Read 7920 times) 

cuckoo
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about matrix approximation
« on: Apr 5^{th}, 2009, 9:07am » 
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SVD solves the matrix approximation problem under Frobenius norm. What if the matrix norm is defined as maximizing number of zero elements? More specifically, given a matrix A, and a specified rank r (r<rank(A)). Find a matix B such that rank(B)=r and B maxizes the number of zero elements in AB.

« Last Edit: Apr 5^{th}, 2009, 9:11am by cuckoo » 
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william wu
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Re: about matrix approximation
« Reply #1 on: Aug 9^{th}, 2010, 12:00pm » 
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Suppose the matrices are m by n. Is it correct to say that no generality is lost in assuming that B_ij = 0 or B_ij = A_ij? In which case, we could bruteforce through all 2^(mn) possible matrices for B, and pick the one such that the number of zeros in A  B is maximized, and rank(B) = r. The only concern is whether or not we can find B such that rank(B) = r under the above assumption.


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