We propose singular value decomposition (SVD) algorithms for very large-scale matrices based on a low-rank tensor decomposition technique called the tensor train (TT) format. By using the proposed algorithms, we can compute several dominant singular values and corresponding singular vectors of large-scale structured matrices given in a low-rank TT format. We propose a large-scale trace optimization problem, and in the proposed methods, the large-scale optimization problem is reduced to sequential small-scale optimization problems.We show that the computational complexity of the proposed algorithms scales logarithmically with the matrix size if the TT-ranks are bounded. Numerical simulations based on very large-scale Hilbert matrix demonstrate the effectiveness of the proposed methods.
CITATION STYLE
Lee, N., & Cichocki, A. (2014). Big data matrix singular value decomposition based on low-rank tensor train decomposition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8866, pp. 121–130). Springer Verlag. https://doi.org/10.1007/978-3-319-12436-0_14
Mendeley helps you to discover research relevant for your work.