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