Deep-QLP: A Low-Rank SVD Approximation for Scientific Machine Learning
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Singular Value Decomposition (SVD) is a fundamental tool in data analysis and machine learning. Starting from the Stewart’s QLP decomposition, we propose an innovative Deep-QLP decomposition algorithm for efficiently computing an approximate SVD. We explore the application of a variant of Deep-QLP, that computes an approximation of all the singular values given a prescribed value of the smallest one, therefore automatically providing the numerical rank. This variant is applied within the framework of Random Projection Operator Networks (RandONets)—shallow architectures that employ random projections and numerical analysis techniques to learn linear and nonlinear operators efficiently and accurately.