Deep-QLP decomposition: theoretical aspects and applications
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In numerous problems across physics and machine learning, such as regularization techniques, dimensionality reduction, network analysis, the identification, and analysis of the singular values and their respective singular vectors of a given matrix play a crucial role. We present Deep-QLP as a novel algorithm that computes an approximation of the singular value decomposition (SVD), given a user-defined tolerance. The algorithm is based on the original Stewart QLP decomposition and its iterative version. The obtained approximation offers a computationally efficient alternative scenario in which the full singular value decomposition could be prohibitive. Deep-QLP can be employed to construct an approximate truncated SVD as well as an approximate pseudoinverse by only using the smallest needed singular components. The Deep-QLP algorithm can also be successfully used in combination with randomized projections, for better performances in the case of sparse matrices.