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

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Problem 6.1. Suppose A = [[S; M1, M2, M3 ]] and that each Mi has more rows than columns. If Mi = QiRi is a QR factorization, then A = [[S; Q1, Q2, Q3 ]] ×1R1 ×2R2 ×3R3 can be regarded as a QR factorization of A. Write a Matlab function [Q,R] = tensorQR(A) that carries out this decomposition where A, Q and R are ttensors. ⊗ Transition to Computational Multilinear Algebra ⊗ Lecture 6. The Tucker Representation
The Tucker Product Approximation Problem Definition Given A ∈ IR n1×n2×n3 and r ≤ n, determine S ∈ IR r1×r2×r3 the “core tensor” U1 ∈ IR n1×r1 orthonormal columns U2 ∈ IR n2×r2 orthonormal columns U3 ∈ IR n3×r3 orthonormal columns such that A − X F is minimized where r X = [[ S; U1, U2, U3 ]] = S(j) · U1(:, j1) ◦ U2(:, j2) ◦ U3(:, j3) j=1 We say that X is a length-r Tucker tensor. In the matrix case, we solve this problem by truncating A’s SVD. ⊗ 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 13: Matlab Tensor Toolbox: Tucker Tenso
Page 17 and 18: The Truncated HOSVD Look at A ≈ A
Page 19 and 20: Problem 6.2. Does this inequality h
Page 21 and 22: The Tucker Product Approximation Pr
Page 23 and 24: The Tucker Product Approximation Pr
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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