A Multilinear Singular Value Decomposition

P R E S E N T B Y B I N G - H S I O U S U N G

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  Main Ideal : Image Compression N M MN pixels (or data) => M+N data ？

Singular Value Decomposition spaces

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

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.

Outline   Singular Value Decomposition(SVD) High-Order Singular Value Decomposition (HOSVD)

Problems Processing     a -> Scalar A -> Vector A -> Matrix -> High-order Tensor

Tensors Expression

Example

Some Basic Definition

Multiplication of a High-Order Tensor

Multiplication of a High-Order Tensor

 Matrix SVD A Multilinear SVD  Nth-order SVD

Solving Multilinear SVD