Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...

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The Tucker Product Representation (Brief Review) When the U’s are from the Modal Unfolding SVDs... Suppose A ∈ IR n1×n2×n3 is given. If are SVDs and then is the higher-order SVD of A. A (1) = U1Σ1V T 1 A (2) = U2Σ2V T 2 A (3) = U3Σ3V T 3 S = A × 1 U T 1 × 2 U T 2 × 3 U T 3 , A = [[ S ; U1, U2, U3 ]] ⊗ Transition to Computational Multilinear Algebra ⊗ Lecture 6. The Tucker Representation
Matlab Tensor Toolbox: Tucker Tensor Set-Up n = [5 8 3]; m = [4 6 2]; F = randn (n(1) ,m (1)); G = randn (n(2) ,m (2)); H = randn (n(3) ,m (3)); S = tenrand (m); X = ttensor (S ,{F,G,H }); Fsize = size (X.U {1}); Gsize = size (X.U {2}); Hsize = size (X.U {3}); Ssize = size (X. core ); s = size (X); A ttensor is a structure with two fields that is used to represent a tensor in Tucker form. In the above, X.core houses the the core tensor S while X.U is a cell array of the matrices F , G, and H that define the tensor X. Variable Value Fsize [5,4] Gsize [8,6] Hsize [3,2] Ssize [4 6 2] s [5 8 3] ⊗ Transition to Computational Multilinear Algebra ⊗ Lecture 6. The Tucker Representation
Page 1 and 2: From Matrix to Tensor: The Transiti
Page 3 and 4: What is This Lecture About? Approxi
Page 5 and 6: What is This Lecture About? The Pla
Page 7 and 8: The Tucker Product Representation (
Page 9 and 10: The Tucker Product Representation (
Page 11: The Tucker Product Representation (
Page 15 and 16: The Tucker Product Approximation Pr
Page 17 and 18: The Truncated HOSVD Look at A ≈ A
Page 19 and 20: Problem 6.2. Does this inequality h
Page 25 and 26: Alternating Least Squares Framework
Page 27 and 28: The Order-d Case The Tucker Product
Page 29 and 30: Matlab Tensor Toolbox: The Function
Page 31 and 32: More on Tensor Rank k-Rank If A ∈
Page 33 and 34: Problem 6.9. Does it follow that th

Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...

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