Compressed Randomized Utv Decompositions for Low-rank Matrix Approximations in Data Science

Abstract

In this work, a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV) decomposition along with a CoR-UTV variant aided by the power method technique is proposed. CoR-UTV computes an approximation to a low-rank input matrix by making use of random sampling schemes. Given a large and dense matrix of size m × n with numerical rank k, where k ≪ min{m, n}, CoR-UTV requires a few passes over the data, and runs in O(mnk) floating-point operations. Furthermore, CoR-UTV can exploit modern computational platforms and can be optimized for maximum efficiency. CoR-UTV is also applied for solving robust principal component analysis problems. Simulations show that CoR-UTV outperform existing approaches.