920 research outputs found
Optimal Column-Based Low-Rank Matrix Reconstruction
We prove that for any real-valued matrix , and
positive integers , there is a subset of columns of such that
projecting onto their span gives a -approximation
to best rank- approximation of in Frobenius norm. We show that the
trade-off we achieve between the number of columns and the approximation ratio
is optimal up to lower order terms. Furthermore, there is a deterministic
algorithm to find such a subset of columns that runs in arithmetic operations where is the exponent of matrix
multiplication. We also give a faster randomized algorithm that runs in arithmetic operations.Comment: 8 page
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