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Low-rank matrix approximation is a fundamental tool in data analysis forprocessing large datasets, reducing noise, and finding important signals. Inthis work, we present a novel truncated LU factorization calledSpectrum-Revealing LU (SRLU) for effective low-rank matrix approximation, anddevelop a fast algorithm to compute an SRLU factorization. We provide bothmatrix and singular value approximation error bounds for the SRLU approximationcomputed by our algorithm. Our analysis suggests that SRLU is competitive withthe best low-rank matrix approximation methods, deterministic or randomized, inboth computational complexity and approximation quality. Numeric experimentsillustrate that SRLU preserves sparsity, highlights important data features andvariables, can be efficiently updated, and calculates data approximationsnearly as accurately as possible. To the best of our knowledge this is thefirst practical variant of the LU factorization for effective and efficientlow-rank matrix approximation.

An Efficient, Sparsity-Preserving, Online Algorithm for Low-Rank Approximation