Low-Rank Approximation and Regression in Input Sparsity Time
نویسندگان
چکیده
منابع مشابه
Low-Rank PSD Approximation in Input-Sparsity Time
We give algorithms for approximation by low-rank positive semidefinite (PSD) matrices. For symmetric input matrix A ∈ Rn×n, target rank k, and error parameter ε > 0, one algorithm finds with constant probability a PSD matrix Ỹ of rank k such that ‖A− Ỹ ‖2F ≤ (1+ε)‖A−Ak,+‖ 2 F , where Ak,+ denotes the best rank-k PSD approximation to A, and the norm is Frobenius. The algorithm takes time O(nnz(A...
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Given a matrix M with n rows and d columns, and fixed k and ε, we present an algorithm that in linear time (i.e., O(N)) computes a k-rank matrix B with approximation error ‖M−B‖2F ≤ (1+ ε)μopt(M, k), where N = nd is the input size, and μopt(M, k) is the minimum error of a k-rank approximation to M. This algorithm succeeds with constant probability, and to our knowledge it is the first linear-ti...
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2017
ISSN: 0004-5411,1557-735X
DOI: 10.1145/3019134