Higher-order singular value decomposition (original) (raw)
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one generalization of the matrix singular value decomposition. The HOSVD has applications in computer graphics, machine learning, scientific computing, and signal processing. Some key ingredients of the HOSVD can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, including the HOSVD. The HOSVD as decomposition in its own right was further advocated by L. De Lathauwer et al. in 2000. Robust and L1-norm-based variants of HOSVD have also been proposed.
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| dbo:abstract | In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one generalization of the matrix singular value decomposition. The HOSVD has applications in computer graphics, machine learning, scientific computing, and signal processing. Some key ingredients of the HOSVD can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, including the HOSVD. The HOSVD as decomposition in its own right was further advocated by L. De Lathauwer et al. in 2000. Robust and L1-norm-based variants of HOSVD have also been proposed. As the HOSVD was studied in many scientific fields, it is sometimes historically referred to as multilinear singular value decomposition, m-mode SVD, or cube SVD, and sometimes it is incorrectly identified with a Tucker decomposition. (en) |
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| rdfs:comment | In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one generalization of the matrix singular value decomposition. The HOSVD has applications in computer graphics, machine learning, scientific computing, and signal processing. Some key ingredients of the HOSVD can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, including the HOSVD. The HOSVD as decomposition in its own right was further advocated by L. De Lathauwer et al. in 2000. Robust and L1-norm-based variants of HOSVD have also been proposed. (en) |
| rdfs:label | Higher-order singular value decomposition (en) |
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