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A Multilinear Singular Value Decomposition

A Multilinear Singular Value Decomposition. Present by Bing- Hsiou Sung. Outline. Singular Value Decomposition(SVD) High-Order Singular Value Decomposition (HOSVD). Outline. Singular Value Decomposition(SVD) High-Order Singular Value Decomposition (HOSVD). Singular Value Decomposition.

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A Multilinear Singular Value Decomposition

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  1. A Multilinear Singular Value Decomposition Present by Bing-Hsiou Sung

  2. Outline • Singular Value Decomposition(SVD) • High-Order Singular Value Decomposition (HOSVD)

  3. Outline • Singular Value Decomposition(SVD) • High-Order Singular Value Decomposition (HOSVD)

  4. Singular Value Decomposition • Main Ideal : Image Compression N M MN pixels (or data) => M+N data ？

  5. Singular Value Decomposition • Linear Transformation • Matrix spaces

  6. Singular Value Decomposition V -> G’s Row Space U -> G’s Column space

  7. Singular Value Decomposition • U->F is similar to V->F. • U makes linear combination of rows of F. • V makes linear combination of columns of F.

  8. Outline • Singular Value Decomposition(SVD) • High-Order Singular Value Decomposition (HOSVD)

  9. Problems Processing • a -> Scalar • A -> Vector • A -> Matrix • -> High-order Tensor

  10. Tensors Expression

  11. Example

  12. Some Basic Definition

  13. Multiplication of a High-Order Tensor

  14. Multiplication of a High-Order Tensor

  15. A Multilinear SVD • Matrix SVD • Nth-order SVD

  16. Solving Multilinear SVD

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