Study of Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations in Data Science
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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.
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