Abstract
We propose two randomized tensor algorithms for reducing multilinear tensor rank. The basis of these randomized algorithms is from the work of Halko et al. (SIAM Rev 53(2):217–288, 2011). Here we provide some random versions of the higher order SVD and the higher order orthogonal iteration. Moreover, we provide a sharp probabilistic error bound for the matrix low rank approximation. In consequence, we provide an error bound for the tensor case. Moreover, we give several numerical examples which includes an implementation on a MRI dataset to test the efficacy of these randomized algorithms.
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Acknowledgements
C.N. would like to thank Shannon Starr for pointing out some important references. We would also like to thank the reviewers for their valuable suggestions and comments.
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Navasca, C., Pompey, D.N. (2015). Random Projections for Low Multilinear Rank Tensors. In: Hotz, I., Schultz, T. (eds) Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-15090-1_5
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DOI: https://doi.org/10.1007/978-3-319-15090-1_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15089-5
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