Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...
Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...
Lecture 6. The Tucker Representation - Gene Golub SIAM Summer ...
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<strong>The</strong> <strong>Tucker</strong> Product <strong>Representation</strong> (Brief Review)<br />
As a Sum of Rank-1 Tensors...<br />
If S ∈ IR r1×r2×r3 , U1 ∈ IR n1×r1 , U2 ∈ IR n2×r2 , U3 ∈ IR n3×r3 , and<br />
then<br />
X =<br />
r1<br />
j1=1<br />
r2<br />
j2=1<br />
X = [[ S ; U1, U2, U3 ]]<br />
r3<br />
S(j1, j2, j3) · U1(:, j1) ◦ U2(:, j2) ◦ U3(:, j3)<br />
j3=1<br />
⊗ Transition to Computational Multilinear Algebra ⊗ <strong>Lecture</strong> <strong>6.</strong> <strong>The</strong> <strong>Tucker</strong> <strong>Representation</strong>
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