We compute the singular values of an m x n tall and skinny (m >> n) sparse matrix A without dependence on m, in the case that m is very large. In particular, we give a simple nonadaptive sampling scheme where the singular values of A are estimated within relative error with high probability. Our proven bounds focus on the MapReduce framework which has become the de facto tool for handling such large matrices that cannot be stored or even streamed through a single machine. On the way, we give a general method to compute A^TA. We preserve singular values of A^TA with \epsilon relative error with shuffle size O(n^2/\epsilon^2) and reduce key complexity O(n/\epsilon^2). We further show that if only specific entries of A^TA are required, then we can reduce the shuffle size to O(n \log(n) / s) and reduce key complexity to O(\log(n)/s), where s is the minimum cosine similarity for the entries being estimated. All of our bounds are independent of m, the larger dimension.
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