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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$\begingroup$ 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. $\endgroup$– Steve HuntsmanDec 18, 2012 at 15:06
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$\begingroup$ @Steve Hi Steve I changed my question a little, hope than will help. $\endgroup$– gstar2002Dec 18, 2012 at 15:51
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