  Low-rank matrix approximation is a fundamental tool in data analysis for
processing large datasets, reducing noise, and finding important signals. In
this work, we present a novel truncated LU factorization called
Spectrum-Revealing LU (SRLU) for effective low-rank matrix approximation, and
develop a fast algorithm to compute an SRLU factorization. We provide both
matrix and singular value approximation error bounds for the SRLU approximation
computed by our algorithm. Our analysis suggests that SRLU is competitive with
the best low-rank matrix approximation methods, deterministic or randomized, in
both computational complexity and approximation quality. Numeric experiments
illustrate that SRLU preserves sparsity, highlights important data features and
variables, can be efficiently updated, and calculates data approximations
nearly as accurately as possible. To the best of our knowledge this is the
first practical variant of the LU factorization for effective and efficient
low-rank matrix approximation.
