1. PRESENT BY BING-HSIOU SUNG A Multilinear Singular Value Decomposition

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 M N MN pixels (or data) => M+N data ？

5. Singular Value Decomposition Linear Transformation spaces Matrix

6. Singular Value Decomposition V -> G’s Row SpaceU -> 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

15. A Multilinear SVD Matrix SVD Nth-order SVD

16. Solving Multilinear SVD