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Concretely if I use the first k eigenvectors find by PCA with a point set A,to project another sparse vector b to k dimension subspace, then use L1-magic to recover b. Will this be better than a Random Projecton. L1-magic is a software tool for compress sensing. b is not a vector from A, but possibly have the same distribution of A.

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Can you flesh this question out a bit? For example, where does b come from (is it an element of A)? What is L1magic--some kind of compressed sensing software? etc. – Steve Huntsman Dec 18 '12 at 15:06
    
@Steve Hi Steve I changed my question a little, hope than will help. – gstar2002 Dec 18 '12 at 15:51

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