Low-rank-ν approximation A ν to the data matrix A Now, we employ the SVD to compress the data matrix A by finding a low-rank approximation. We define the "best" rank ν < r approximation to A, A ν , as the one where ||A -A ν || F is minimized, where || • || F is the Frobenius norm. One can show that the optimal rank-ν approximator is: