Out-of-core singular value decomposition
Vadim Demchik, Miroslav Ba\v{c}\'ak, Stefan Bordag

TL;DR
This paper presents a scalable, out-of-core randomized SVD algorithm capable of efficiently factorizing very large matrices that exceed main memory, with features like parallelization, load balancing, and resumability.
Contribution
It introduces an innovative out-of-core randomized SVD method that handles large matrices efficiently, supporting parallel processing and interruption recovery.
Findings
Handles arbitrarily large dense and sparse matrices
Supports parallel and out-of-core processing
Enables resumption of interrupted computations
Abstract
Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However, many common problems involve very large matrices that cannot fit in the main memory of commodity computers, making it impractical to use standard SVD algorithms that assume fast random access or large amounts of space for intermediate calculations. To address this issue, we have implemented an out-of-core (external memory) randomized SVD solution that is fully scalable and efficiently parallelizable. This solution factors both dense and sparse matrices of arbitrarily large size within arbitrarily small memory limits, efficiently using out-of-core storage as needed. It uses an innovative technique for partitioning matrices that lends itself to…
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Taxonomy
TopicsMatrix Theory and Algorithms · Tensor decomposition and applications · Sparse and Compressive Sensing Techniques
