Streaming Low-Rank Matrix Approximation with an Application to Scientific Simulation
For scientists and engineers needing real-time compression of large-scale simulation or sensor data, this method provides more accurate and robust low-rank approximations.
The paper introduces a new streaming algorithm for low-rank matrix approximation that achieves smaller relative errors and is less sensitive to parameter choices than prior methods, demonstrated on Navier-Stokes simulation and sea surface temperature data.
This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm for constructing an accurate low-rank approximation of a matrix from streaming data. This method is accompanied by an a priori analysis that allows the user to set algorithm parameters with confidence and an a posteriori error estimator that allows the user to validate the quality of the reconstructed matrix. In comparison to previous techniques, the new method achieves smaller relative approximation errors and is less sensitive to parameter choices. As concrete applications, the paper outlines how the algorithm can be used to compress a Navier--Stokes simulation and a sea surface temperature dataset.